Tractate Peah deals with agricultural gifts the Torah mandates be given to the poor. There are three main passages in the Torah that deal with these gifts. Since they will be relevant throughout the tractate it is worth quoting them fully now.
Leviticus 19:9-10 9 And when you reap the harvest of your land, you shall not wholly reap the corner of your field, neither shall you gather the gleaning of your harvest. 10 And you shall not glean your vineyard, neither shall you gather the fallen fruit of your vineyard; you shall leave them for the poor and for the stranger: I am the LORD your God.
Leviticus 23:22 And when you reap the harvest of your land, you shall not wholly reap the corner of your field, neither shall you gather the gleaning of your harvest; you shall leave them for the poor, and for the stranger: I am the LORD your God.
Deuteronomy 24:19-22 19 When you reap your harvest in your field, and have forgotten a sheaf in the field, you shall not go back to fetch it; it shall be for the stranger, for the orphans, and for the widow; that the LORD your God may bless you in all the work of your hands. 20 When you beat your olive-tree, you shall not go over the boughs again; it shall be for the stranger, for the orphans, and for the widow. 21 When you gather the grapes of your vineyard, you shall not glean it after you; it shall be for the stranger, for the orphans, and for the widow. 22 And you shall remember that you were a slave in the land of Egypt; therefore I command you to do this thing.
According to the rabbis there are five agricultural gifts given to the poor: 1) Corners of the field—peah. 2) The gleanings, that which falls to the ground during reaping. 3) Forgotten sheaves. 4) Grape gleanings. 5) Clusters of grapes that were unripe during the first harvesting.