Final Gravity (FG) is the specific gravity reading taken once fermentation has finished — what remains after yeast has consumed the fermentable portion of the wort's sugar, leaving behind unfermentable dextrins, proteins, and whatever the yeast strain simply didn't get to.
"Finished" needs confirming, not assuming
A single gravity reading that looks close to expected isn't proof fermentation is done — the standard check is taking readings on two or three consecutive days and confirming the number holds stable, since an actively fermenting beer sampled mid-process can show a misleadingly "final-looking" number that then keeps dropping. Bottling or kegging too early, based on an unconfirmed reading, risks over-carbonation from residual fermentable sugar still present.
FG is a diagnostic number, not just an ABV input
A finished FG that's noticeably higher than expected for the yeast strain and mash temperature used is often the first sign of a genuine problem — see why is my final gravity stuck at 1.020 for the most common causes, ranging from underpitching to a mash temperature that left too little truly fermentable sugar to begin with. Checking FG against the pitched yeast strain's own published attenuation range is the fastest first diagnostic step before assuming the recipe itself was wrong.