To tout means to praise, boast, or brag about. If you like to tout your skill as a skier, you tell people you can go down expert-level hills.
Sometimes parents will get into bragging wars about their children, each touting the accomplishments of his or her child. Sometimes the word means more of "to claim." The company touted the lotion as a solution to wrinkles. Broccoli has been touted as the cancer-fighting vegetable. In England, a tout is a person who gives advice about gambling. If you're looking to play some money on the ponies, go see the tout who hangs out at Jackie’s bar for a tip.