As a somewhat novice tetris player, I’ve always wondered what Finesse was. My first encounter with the word was on tetr.io, where there are two options related to finesse (restart on fault and sound on fault), and later on jstris.

Finesse refers to the term “Two-Step finesse”, which according to a Hard Drop wiki article is “an input optimization technique used to place down tetrominos while saving keypresses” (https://harddrop.com/wiki/Finesse)

Like the name Two-Step suggests, it means that most actions you take should take two key presses maximum, which means that you have to take advantage of some of the quirks of SRS, such as kicks or the fact that rotations affect the piece’s position.

However, finesse can be learned just by playing tetris, as optimizations like this come naturally as you try getting faster and faster. So in my opinion, putting time aside to learn finesse isn't strictly necessary if you want to go fast, but if you are a newcomer to modern tetris, then I would recommend to practice finesse as a warmup.