The Potters are Harry's deceased parents. When they were young, both attended Hogwarts and were Gryffindors. Voldemort killed them when Harry was a baby, but Harry grows up thinking they died in a car crash. When Harry looks into the Mirror of Erised, it's his parents that he sees reflected there: to know them and to be with them is his heart's desire.
Harry doesn't know much about his parents, except for what other people remember about them. For example, Mr. Ollivander tells Harry that his father was good at Transfiguration and his mother was good at Charms; Hagrid tells Harry that his parents were head boy and girl at Hogwarts. James was a little mischievous, since he was the first owner of the invisibility cloak, but brave and good, since he saved Snape's life. Lily's love for Harry was so powerful that it formed a shield that would always protect him, even after her death.