There are various forms of prayer. The best-known form—and what most people mean when they say “prayer”—is petitionary prayer. That is, petitionary prayer is the act of asking for gifts or graces from God.
This is why our Protestant brethren are scandalized when we say we “pray” to the saints. They say it is wrong to pray to saints, because it treats them as though they were God and had the power to grant gifts or graces.
Put this way, the Protestant argument is correct. It would be wrong to “pray” to the saints if we thought that “praying to the saints” meant that a saint was using their own, self-derivative powers to bring about grace…or if prayer was identical with “worship,” which is for God alone.
This is not, however, the sense we are using when we as Catholics pray to the saints. The word prayer simply means “to ask,” not “to worship.” As the Catholic Encyclopedia clarifies:
[W]hen we pray to [the saints], it is to ask for their intercession in our behalf, not to expect that they can bestow gifts on us of their own power, or obtain them in virtue of their own merit.
—Catholic Encyclopedia
This is what we mean by intercessory prayer: the saints intercede for us. James 5:16 says that “The prayer of a righteous man has great power in its effects.” Since the saints are perfect, and are in heaven with God, their prayers have great efficacy. So we ask them to turn to God on our behalf and ask Him to bestow the proper graces and gifts upon us.
Though our prayers are far less perfect than those of the saints, we can and should intercede for each other, as well. This is what is happening when we promise to pray for someone else—we are practicing intercessory prayer!