Watch out for literary critics. They can get feisty.
A big reason the Formalists got together in the first place was because they were sick and tired of the state of literary criticism in Russia in the early 1900s (and let's face it, people in Russia were pretty sick and tired of everything in the early 1900s—at least, they were until the Bolshevik Revolution of 1917).
As far as the Formalist fellas were concerned, though, everywhere they turned, they found literary critics talking about how this or that poem was an emanation of the author's "soul," or how this or that novel reflected a certain "philosophical" or "psychological" viewpoint. Pretty dry, huh?
So the Formalists asked, why the borsht are we looking outside the text to try to explain it? We shouldn't have to do psychology or philosophy to explain a work of literature. We should be doing literary criticism. Which means, they argued, that the focus should be brought back to the text itself. Throw all that other stuff—authorial biography, cultural context, philosophical context, politics—out the window. Let's just look at the text, ladies and gentlemen.
Which is exactly what they went on to do. Of course nowadays we're used to looking very closely at a text as soon as we start studying for the SAT in second grade, but back when the Formalists started doing it, it was new. What was especially new was the Formalists' really rigorous focus on language and the linguistic components of a text. These guys were obsessed with studying syntax, grammatical construction, and the sounds of words, and how all that stuff functioned in poetry.
For them, literature was made up of a sum of "devices." Does a machine pop into your head when you hear the word "device"? Well they meant that, but in books.
A literary "device" might be anything from metaphor to repetition to parallelism and beyond. The Formalists said that we need to identify these devices and investigate how they're operating or functioning in a given text. And by doing that, we can understand any literary text, without having to go off and research the author's biography or some obscure philosophical theory that he or she was really into.
The Formalists took their literary investigation so seriously that they thought of it as a "scientific" endeavor. They believed that they were the equivalent of those scientists in white coats doing experiments in labs. Okay, so maybe they weren't working with chemical or biological elements. They were working with literary elements. But hey, what's the difference anyway?