I'll try to give some details of my own experiences, Tao, though it will make me look like a mad woman. LOL
I can try to offer up some explanations, but to be honest, I don't have a ton of them- just vague ideas. I haven't invested as much time into thinking of explanations as I have into figuring out how to open up to doing it and using the information I gain.
First, I'd recommend a book of stories about this sort of thing: Kinship with All Life.
Amazon.com: Kinship with All Life : Simple, Challenging, Real-Life Experiences Showing How Animals Communicate with Each Other and with the People Who Understand Them: J. Allen Boone: Books
On horses...
I've been working intensively with horses for about 11 years now. I had long communicated through riding and groundwork, learning to use body language as one of them rather than as a predator, so that I could more easily train them. But about six years ago, perhaps (I forget), I first had an actual exchange with a particular horse. I was cleaning the stall of a new mare that came in. I began receiving images and feelings from her. I have had this happen before with humans, but it's not quite the same. Horses largely communicate through (from what I've seen) is near instantaneous sharing of visceral feelings- what you might call "gut" reactions. You feel things from them first in your body, not your brain. You might feel their anxiety, fear, quiet, enjoyment and it radiates from your muscles and thorax to your brain- you feel it before you recognize the feeling you have been given. It makes a lot of sense if you consider that they are prey animals- the communication is first through feeling to the entire herd (and you) and this allows rapid and compelling communication of danger or pleasure. However, horses do more than that. They send images. The images are not like a human would send, associated clearly with a single thought that could translate into words. The images evoke feelings and a sort of gestalt of what is going on in the horse's head, not a particular train of thought. So far as I can tell, horses just don't think like us- they don't think linearly. It's all in free-association and big picture. Because of this, my own opinion is those animal communicators that get paid the big bucks (I've seen people shell out $100 per reading at show barns) and are telling people "Oh, your horse likes purple" (horses can't see purple) or "Your horse thought XYZ the other day" are talking total BS. This is not how horses think, what they care about, or what is useful communication to them. How horse to horse and horse to human communcation works in this way, I have no idea. I could say vaguely that everything seems connected energetically to allow this, or something about bioenergetic fields, but to be honest I have no earthly idea how I pick up on that stuff. And I am not entirely consistent- my mind has to be pretty clear to pick up on images. Feelings are easier. Incidentally, it's the same way with people- I only pick up on thoughts when people are "yelling" in their head or when my mind is exceptionally clear of my own noise. But I pick up on feelings and general senses of intent all the time.
In terms of the flip side, horses are incredibly sensitive to intention and thought (of course to varying degrees by individual). Many breeds that were created to live very closely with humans, such as Arabians, are so intensely sensitive to their human companions that they are mistakenly thought to be "crazy" or "unpredictable." In fact, they are very predictable. They mirror their human companion's emotions and intent so well and so quickly that the human has often not consciously recognized his/her own thoughts until they are present in the horse, which is nearly instantaneous. If you feel tense, the horse tenses- typically in the same spot of the body. If you imagine the horse doing a poor transition, he does. If you imagine a perfect transition, he does. If you even consider "halt," the horse has already stopped. If you are angry, even if you act OK and other humans would think you're being normal, the horse will react in fear of your anger. You can't fool them- they are like living lie detectors in terms of your focus and emotional state. How this works is to me pretty obvious- your intentions and emotions, when at a sub-conscious level, are already influencing your heartrate, pupil dilation, breathing, posture, muscle tone, etc.- and horses are extremely sensitive to this. Anger comes through your body as threat, fear comes through as danger, pleasure or relaxation comes through as confidence. And when you think sub-consciously to stop or trot or whatever, your body is already moving to prepare for this motion even when you haven't consciously told it to yet. I don't know if they receive images from us the way we can from them.
I later read a book, The Tao of Equus, in which the woman experienced something similar. So that was interesting- could be she and I just have similar personality types (and madnesses LOL), but on the flip side, it could be that those who are sensitive in this way pick up on the same communication styles from other beings.
Amazon.com: The Tao of Equus: A Woman's Journey of Healing and Transformation through the Way of the Horse: Linda Kohanov: Books
So far as I can tell, dogs and cats are similar, but they are more linear in thinking. They can form a plan. They're more like us, which makes sense to me, given that they (like us) are ominvorous and/or predatory, which takes a lot more planning than prey animals and yet necessitates less immediate communication of danger. But though I am very close to my dogs and my kitty I had for 20 years (now passed away), I must confess that I haven't put as much work into trying to communicate that way with them. It sort of evolved on its own with the horses because I was working many different horses and spending hours and hours each week doing it.
On insects...
I dislike killing things. And I dislike insects. So after reading "Kinship with All Life," I had the new idea to communicate my needs to insects- mostly about them peaceably leaving my personal bubble.
For the most part, it works. Spiders, beetles, crickets- all are pretty good listeners. I either ask them to leave on their own, or if I need them to be gone immediately, I get a cup and ask them to get in the cup. I reassure them about what I'm doing, and take them outdoors and release. My husband doubted my insect-communication skills until one day I was asking a cricket to get in the cup and the cricket jumped from the floor into my cup- I was standing so he jumped about four feet directly into the cup, then stayed there until I got him outside, after which he jumped out of the cup. Could be a coincidence... or maybe I am a cricket-whisperer. LOL By the way, if anyone has tips on communicating with roaches- let me know. They have never, ever listened. LOL
On trees...
Trees do not give me images or thoughts, but rather feelings. Complex feelings, like the sort you might have after a vivid dream as you wake up and forget what you were dreaming about or the kind you get when you can't quite remember an event but you call up the mix of thoughts and emotions you had at the time. Trees also give me a sort of wisdom- they are teachers. I wouldn't say they transmit ideas as much as inspire them. They have an energy to them- the Redwoods have a low sort of hum that is so overwhelming that it brings me to tears. And the Bristlecone Pines feel like they are very quiet, patient trees. Individual trees feel different, but so do entire species or, I should say, genera. Some trees have more going on in there- almost like being a person and coming closer to images or thoughts- they tend to be older trees. I don't know why, but plants gain more ability to communicate as they get older, or so it seems. The oldest are like mentors and comforters, though they can feel bristly at first until one gets to know them and they understand you are respectful and won't cause harm. Then they tend to be quite parental.
Trees are like crystals in a way, as they have a certain "hum" to them, a certain energy. Crystals don't impart feelings though- more like energy (in the literal sense- like feeling different kind of electrical zaps at different intensities and frequencies). However, different rocks will have an effect on me- but it is more mechanical than personable.
I have heard from some that bodies of water have a sort of consciousness, but I haven't been able to experience that yet. I suspect it is partly because I am a woods-person more than a water-person, so I am rarely spending time with rivers or lakes. The sea certainly seems to me like it has a great big consciousness- it generally makes me giddy with happiness as it feels like I can breathe with it and feel the vastness of what it would be like to be such a being. Places seem to have memories, but not necessarily personalities. The feelings and images I get from places are tied to past. I'd guess this is a sort of energetic signature of some sort- don't know how to describe that. Places also have different energies- kind of like rocks- but this may be tied to the earth's energetic field or (a pet idea of mine, though entirely unfounded) points at which the earth's (and our universe's) plane touches another- this goes along with a sort of multiverse concept in which the various universes might be intersecting but largely unaware of each other.
So there's my long ramblings on the subject. None of it is scientific and most of the explanatory ideas (outside of body language with horses) are just ponderings I've had without much time given to them.