The Restoration period begins with the ending of Puritan rule and the restoration of the Stuart monarchy with the crowning of Charles II in 1660. It is difficult to discern when, exactly, the "Restoration" period ends--some scholars group it together with the entire 1700s and call it the Long Eighteenth Century, while others assert that the Restoration itself had ended by the late 1600s. In many ways, the Restoration marks a distinct break with the styles and tastes held before.
One of the major literary modes during the Restoration was drama. Charles II lifted a prior Puritan ban on theater in England, and seeing plays became extremely popular. Unlike Elizabethan drama (think Shakespeare and Marlowe), which was filled with complex characters and elaborate poetry, the theater of the Restoration (and the ensuing eighteenth century) was much less complex. Nearly all of the characters are one of a number of "types" or tropes: there's the self-absorbed fop, the libertine, the resourceful woman, the seductress, the virgin, the fool, etc. In addition, many Restoration plays are much more bawdy and comedic than the prior Elizabethan. Some famous Restoration and early eighteenth-century plays are Wycherly's The Country Wife and Congreve's The Way of the World. I highly recommend Restoration and eighteenth-century drama--these plays are seriously fun reads.
The poetry of the Restoration period is also a distinct break from the Elizabethan sonnet cycles of Shakespeare and Sydney. Many of the poems take the form of satire, often about the changing political atmosphere that characterized the Restoration. A famous example of political satire is Dryden's Absalom and Achitophel, which uses Biblical allegories to describe the current political atmosphere.
One writer who spans both the Puritan and Restoration periods is John Milton. Though he was certainly writing during the Restoration (Paradise Lost was published in 1666), he is not considered a Restoration poet because he is so pervasive and has spanned such a long period (Lycidas was written, I believe, in 1637, far before the execution of Charles I). Milton, as a Puritan himself, was writing against the restoration of monarchy: he published Eikonoklastes after the execution of Charles I, warning of the dangers of restoration; in this way, even though Milton is not considered part of the Restoration movement, he is still responding to the turbulent atmosphere characterizing Puritan rule and the subsequent return to monarchy.