The speaker of this poem is a really complicated guy. He'd give Freud a run for his money, we think. But we're getting ahead of ourselves with all this psychoanalysis stuff; first, we should point out the obvious. The speaker has spent a lot of time hunting, or really likes hunting, or likes talking about hunting. Nearly every line is the poem says something about… yep, hunting. He also knows Latin, which tells us he's probably educated (maybe an English courtier?). After all, the average person in the Renaissance didn't really know Latin.
In addition to all of this (the penchant for hunting and the Latin), the speaker has a good sense of right and wrong, or rather he knows what he shouldn't do. He knows the deer belongs to somebody else and that chasing it could land him in a lot of hot water, which is why he resolves to quit: "I leave off, therefore" (7).
Dutiful though he is, our speaker is still torn between two extremes. This is where our boy Sigmund Freud could help us out. The speaker knows he must stop chasing this darn deer, and yet his desire is still so powerful. He goes back and forth. At first he says he may hunt no more (2) because he's tired and weary and can't have her; then he says he's still part of the hunting party (in other words, still chasing) and just can't take his eyes off of her, and then he says he's gonna quit. It's like, make up your mind already, dude.
Okay, okay—maybe that's a little harsh, but the speaker is clearly a textbook example of the power of desire. His little back-and-forth routine tells us that he's a guy who wants to do what he should, and yet also wants to do whatever he wants. He seems to know this, which is why he comes off as kind of a sad and melancholy dude. He wants something he can't have, and that's a tough bind to be in.