Mount Purgatory has seven terraces in Dante’s Purgatorio, each devoted to purging one of the seven deadly sins. The terraces are pride, envy, wrath, sloth, avarice, gluttony, and lust.
They form the central portion of the mountain. Before reaching them, Dante passes through Ante-Purgatory, where souls delayed in repentance wait on the lower slopes. After the seventh terrace, he reaches the Earthly Paradise at the summit.
The terraces reflect Dante’s moral theory of love. The first three correct love directed harmfully toward others; the fourth represents deficient love, or sloth; and the final three correct excessive or disordered love of earthly goods. Each terrace therefore combines punishment with spiritual education.
A common mix-up is counting Ante-Purgatory or the Earthly Paradise as additional terraces. Those are distinct regions, so the canonical answer to the question is seven.