Pope wrote in rhymed heroic couplets.
This is an understatement. He was considered the master of all time of all universes of the heroic couplet.
Um, what is a heroic couplet, you ask? It's a couple of lines (two, to be exact) that are rhymed. And they are in iambic pentameter (that's five pairs of unstressed and stressed syllables. It sounds like ba-DUM ba-DUM ba-DUM ba-DUM ba-DUM).
It's important that this poem is written in heroic couplets because it is the ideal form of the neoclassical poets – yes, Pope was considered the best one of these. Neoclassical means "new" classical. And "classical" refers to all things from ancient Greece and Rome. The Neoclassical poets put the ancient Greek and Roman poets on a pedestal and tried to write like them (except in English – but you knew that). Writing "Sound and Sense" in heroic couplets was a statement; with this form Pope's readers would know that he meant business. He was engaging the hot literary topics of the day, paying respect to the ancients, and at the same time putting his own stamp on the history of literary criticism.
This poem is also fourteen lines longs, which means it might be a sonnet. We say might because it doesn't follow any of the other sonnet rules. We could call it a quatorzain (from the French word for fourteen), but hey, not many people actually use this term anymore.