An der großen Kreuzung biegen Sie dann nach rechts ab.
In this sentence, what does the ab mean? I don't think it is meant to split off.
Oh by the way, while we're at it, what is nach there for as well? I know nach can mean turn, but I thought biegen was there for that?
"Ab" is a part of verb "abbiegen". It's a separable verb therefore "ab" is in the end of the sentence.
"Nach" never means "turn". It means (in this case) "to" (in other cases "nach" can mean f.e. "after"). Your confusion might be based on the expression like "nach links" which you understand as "turn to the left", but the correct translation would be just "to the left".
The word abbiegen basically consists of two parts: The prefix ab- and the root biegen.
There are a lot of words in German with prefixes like that. For example:
In English you would say "Shoot them down!" or "Work it off.". So you do in German: "Schießt sie ab!" or "Arbeitet es ab.".
But sometimes a verb loses this extra bit, but not very often.
To remove has no extra bit, but to take off has; thus being closer to one possible translation: abnehmen.
