It tells us that, although she may be highly unconventional in some respects, there are limits to her transgressions. Hermia is deeply in love with Lysander and doesn't want to consummate that love until they are married. The main reason why she chose to run off with Lysander to the forest in the first place was because she wouldn't have been able to marry him back in Athens due to her father's disapproval.
For his part, Lysander insists that his intentions are honorable. He simply wants to sleep by Hermia's side. But Hermia doesn't want to take any chances, so she insists that Lysander sleep apart from her in order to preserve their modesty. This tells us that Hermia is clearly a virtuous woman by the standards of her day, and she takes her virtue very seriously indeed.
This question depends heavily on the chosen subtext that the director choses for Hermia in this scene in Act II Scene 2. Certainly the words she says suggest that her refusing to sleep too close to Lysander shows that she is a modest and respectful woman, not wishing to violate the rules of her society and culture. However, a director could chose to have Hermia deliver those lines in a much more flirtatious way through use of body language and tone of voice to present a character who is using her sexuality to lead Lysander on and play with him.
But gentle friend, for love and courtesy
Lie further off, in human modesty;
Such separation, as may well be said,
Becomes a virtuous bachelor, and a maid,
So far be distant, and good night sweet friend;
Thy love ne'er alter, till thy sweet life end.
So you need to ask yourself how, if you were the director, you would direct Hermia in this scene. It all comes back to the question of subtext and how you interpret it.