Neoclassicism generally refers to any artistic movement that seeks to recreate the ideals of what are broadly known as Classical Greece and Rome--in other words, the art of the Greeks and Romans of antiquity. In English literature the period usually designated neoclassical runs from about 1670 to about 1750, the years in which the two chief poets were John Dryden and Alexander Pope, and the most prominent prose writer was Jonathan Swift. It's also called the Augustan age because these writers self-consciously modeled their work on that of the Latin poets--primarily Virgil, Horace, and Juvenal--at Emperor Augustus's court during his reign from 27 BCE to 14 CE.
The usual aesthetic features we identify in classical and neoclassical art are an adherence to the ideals of balance and elegance, a restraint in the overt expression of emotion, and a cultivation of the genres of didactic poetry (poetry that seeks to teach) and of satire. The following lines from Pope's Essay on Criticism are often quoted as a motto expressing the ideals of the period:
Tis more to guide, than spur the Muse's steed,
Restrain his fury, than provoke his speed,
The Winged Courser, like a gen'rous horse,
Shows most true mettle when you check his course.
During the period, the heroic couplet (rhymed iambic pentameter) became standard. Dryden's and Pope's work consisted of satires, mock-epic or mock-heroic poetry (a genre in which the tone and diction of epic poetry are ironically used for trivial and comic subjects in a satiric way), philosophical and didactic poems such as Pope's Essay on Criticism and Essay on Man, and translations of Virgil (by Dryden) and Homer (by Pope). Swift wrote prose satires and is, of course, best known for Gulliver's Travels.
Though there are exceptions, the trend during this period was for writers to avoid expressing their own personal or idiosyncratic emotions. The emphasis instead was on universal concerns, matters to which humanity in general could relate and which could "elevate" mankind either through explicit didacticism or satire, in which human follies were held up to ridicule. This was also the period in which the English began to see their literature as having international significance and greatness. Both Shakespeare and Milton came to be seen as the two principal iconic English writers, in spite of the fact that their work did not conform to neoclassical ideals. However, in invoking classical Greece and Rome as their ideal, the neoclassical poets had also developed a sense of their own culture's ability to create art that would be permanent in some sense instead of being only transiently of value. They saw not only their own work, but even more that of their greatest writers of the past, as fulfilling this goal.