Where It All Goes Down
The speaker talks about deer hunting in nearly every line of this poem, so we'll go ahead and guess that it's taking place somewhere outside, away from the city—basically a place where you could assemble a large hunting group and find wild deer. It's probably a very scenic, semi-wooded area that you might find in, say, rural England—just a hunch. Maybe it's something like this.
In this picturesque landscape, there are most likely several groups of hunters, many of them associated with the court of Henry VIII and hence rich—expensive clothes, expensive horses, giant entourages. If you're looking for a word to describe these guys (Wyatt included), that word is courtier? Huh?
The word sounds like somebody who hangs around a court and, wouldn't ya know it, that's exactly what it is. You see, lots of rich, connected, aristocratic guys would hang around the courts of royalty like flies, in the hopes of getting more connected. That's how it worked back then. If you were, say, Thomas Wyatt, you would linger around Henry, try to gain his favor, and maybe get a good a good government post in, say, Hawaii (well, not Hawaii exactly, but the sixteenth-century equivalent). Wyatt, for example, was once made ambassador to the Holy Roman Empire. If hanging around could land you connections and good jobs, it could also land you bad jobs, if you annoyed Henry. One false move, and you might end up serving as the equivalent of a garbage man in some undesirable location. Yikes.
Anyway, let's get back to the hunters (who are hunting because hunting is cool, and because spending quality time with the king is a good way to get some brownie points).The groups all leave one after the other, and the speaker is in the last group, the one that "farthest cometh behind." It's not really clear what happens, but we get the impression that the speaker stays in the last group because he doesn't want to be hunting this particular "hind" anymore. When he catches a glimpse of the "hind" he's trying to resist, however, he breaks away from his group and goes after it, fainting, confused, and absolutely in awe of this majestic creature.
The deer flees, but eventually stops. The speaker mistakenly thinks this is a tame creature, and is able to get really close to it. As he approaches, he notices something glimmering around her neck. When he finally gets close, he reads an inscription in diamonds that confirms his worst fears: this deer belongs to someone much more powerful than he and is actually totally wild, even though she seems tame. No matter how much the speaker might enjoy the scenery of his surroundings, the setting here cannot overcome the rigid pecking order of English nobility: don't mess with the king (or the king's possessions), or your next setting might be a jail cell, or worse.