subset
A subset is the part of a typeface a document actually draws, copied into the file in place of the whole typeface.
What the word means
A document that wants to look the same everywhere carries its lettering inside itself. A modern typeface holds thousands of drawn shapes: every accent, every alphabet, every symbol.
An invoice uses perhaps eighty of them. Copying the rest is paying to carry what is never shown. Subsetting keeps the shapes the pages draw and drops the others, and the file gets smaller by a large factor rather than by a few per cent.
What it does on a real document
The examples on this site carry their lettering that way. The tables inside the file that say how wide each letter is are cut down to the same list, which is where a good part of the saving comes from: those tables are longer than the drawings they describe.
What must survive the cut is the way back to the alphabet. A reader has to be able to select a paragraph and paste it elsewhere, and a search has to find a word. A subset that keeps only the drawings gives a page you can look at and not copy.
Where it comes from, and why
The habit is as old as carrying lettering inside a document at all, and it began for two reasons at once. Files travelled on floppy discs and down telephone lines, so their size decided whether they travelled.
The second reason was legal. A typeface is somebody's work, sold under conditions, and sending a whole one inside a document would be sending the goods. A subset carries what one document needs and is not a typeface anybody could use.
See it on a finished document
Fonts kept inside the file A minimal PDF The rules behind this word, and the texts they are read from