The first line sets up the speaker's problem: while an unnamed "they" used to "seek" him, now they "flee" (or run away) from him. Soon enough it will be clear that the speaker is talking about his lovers, but for now things remain vague. A clue as to who this "they" refers to does appear in line 2, however, with the phrase "naked foot." This means barefoot but also suggests sexual intimacy, that the air was charged with excitement whenever "they" sought the speaker out.
The opening lines also set up the poem's extended metaphor/conceit, which portrays love and sex as a kind of hunt. Take the word "stalking," which creates an image of these barefoot creatures prowling around the speaker's chamber as a predator prowls around its prey. The speaker thus uses animalistic language to paint relationships between people as something primal, instinctual, and even dangerous. On that note, it's worth noting that Wyatt was a courtier in Henry VIII's court, which meant that sleeping with the wrong person—or, similarly, being accused of some sexual wrongdoing—really could result in death!
Now, the speaker has apparently fallen out of favor with this "they." He doesn't specify why this has happened, but the context of the poem might again offer some clues: the fragility of personal loyalties and the suspicion that came with this was one of the defining features the English court during the Tudor period (1485-1603).
The sounds of these lines are also notable. Take the assonance between "flee," "me," and "seek," which draws readers' attention to the contrast between the speaker's two states—being fled from and being sought out. Meanwhile, the hissing sibilance throughout these lines ("sometime," "seek," "stalking") conveys a quiet world of whispers and intrigue.
These lines also establish the poem's meter, which is iambic pentameter. This means that each line has five iambs, poetic feet with a da-DUM rhythm:
They flee | from me | that some- | time did | me seek