The previous mitzvah was the positive precept to leave the fallen grapes for the poor. Here, we have the injunction against gathering them. Just as leket – fallen grain – is only one or two ears, peret – the fallen grapes – only applies when the harvester drops one or two from a bunch. (If he dropped his whole load, for example, he would not have to forfeit it. Only the grapes that drop individually may not be retrieved.) The Mishnah tells us that a person who places a basket under the vine while gathering, in order to catch the falling grapes, is considered one who steals from the poor. (See Mishnah Peah 7:3.)
The reason underlying the mitzvah of peret is the same as in the last few mitzvos: When God gives us good things, He wants us to share them with those less fortunate. Not only does this help the needy, it helps us by cultivating the traits of generosity and compassion.
This prohibition applies to both men and women but only in Israel. It is discussed in the seventh chapter of tractate Peah in the Mishnah and is codified in the Shulchan Aruch in Yoreh De’ah 332. It is #213 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #9 of the 26 mitzvos that can only be performed in Israel according to the Steipler Gaon.