Learn French: Elle comprend parfaitement la technique. - She understands the technique perfectly.

It comes from the adjective meaning "perfect". To make the adverb, you take the feminine form of the adjective (parfaite) and add the ending -ment. This is the standard way to create an adverb of manner in French, just like adding "-ly" to an adjective in English!

Why does parfaitement come right after the verb, rather than at the end of the sentence?

In French, adverbs that modify a verb usually go directly after the conjugated verb. While in English we often put it at the end ("She understands the technique perfectly"), French slots it right behind the action: Elle comprend parfaitement...

What verb is comprend from, and how does it conjugate?

It is the il/elle/on form of comprendre (to understand). It conjugates with the exact same pattern as prendre (to take). You drop the -re to get the singular forms: je comprends, tu comprends, elle comprend.

Is the "ent" at the end of parfaitement silent, like it is for plural verbs?

No! The -ent ending on verbs for ils/elles (like elles comprennent) is silent, but the -ment suffix used to create adverbs is always pronounced. It sounds like a nasal "mahn". However, the final "t" in parfaitement is completely silent.