What Is a Sheet?
The line that sets the sail’s angle to the wind — the real boating equivalent of a ‘throttle pedal’ analogy.

A sheet is the line used to set a sail’s angle, and it should not be confused with a halyard: the halyard hoists the sail up, while the sheet controls its angle (trims it). On a sailing boat, the sheet is the one continuous control that determines speed and comfort.
Letting it out correctly by a few centimetres reduces heel and makes the boat faster. It is also a safety line: in a sudden squall, the first thing to do is ease the sheet; that is the brake that depowers the sail.
Rules of thumb
If in doubt, ease it: ease the sheet until you can just see a slight flutter at the luff, then sheet in a touch.
Too much trim creates heel: a sheet hauled in to the stop creates heel, not speed; the usual answer to ‘we’re slow’ is ‘let it go a bit’.
Squall drill: ease the mainsheet first, then ask questions.
Wear in the running gear also makes fine trim harder: the blocks and traveller the sheet runs through pick up salt and become stiff, and a heavy system makes delicate trimming impossible. A hardened sheet that has thinned down will slip both in the hand and in the cleat.