A functional group is the specific cluster of atoms within a larger molecule that's actually responsible for how that molecule reacts. Two molecules can have wildly different carbon skeletons — one a short chain, one a huge ring system — and still react almost identically if they share the same functional group, because the rest of the carbon skeleton is largely just along for the ride, chemically speaking.

This is why organic chemistry courses are organized functional-group by functional-group rather than molecule by molecule: once you know how an alcohol behaves, you know roughly how EVERY alcohol behaves, whether it's a two-carbon molecule or a forty-carbon one. Five functional groups in particular come up so often that they're worth being able to recognize instantly, without hesitation, the moment you see them drawn.

The trickiest distinction among the Big 5 is between an aldehyde and a ketone, because both contain a C=O carbonyl — the only difference is what else is attached to that carbonyl carbon. An aldehyde's carbonyl carbon is bonded to exactly one other carbon (or nothing else at all, as in formaldehyde) and one hydrogen, which is why it's written CHO. A ketone's carbonyl carbon is bonded to two other carbons and no hydrogen at all, which is why it's simply written CO with carbons flanking it on both sides.

That single hydrogen difference has real chemical consequences you'll see throughout this course: aldehydes are generally more reactive toward nucleophilic addition (less steric hindrance, and that C-H can itself be oxidized further to a carboxylic acid), while ketones are comparatively more resistant to oxidation because there's no hydrogen left on that carbon for an oxidizing agent to remove.