Black 1 is a bulge play (fukurami or fukure in Japanese).
It is a hane play, backed up by the marked stone already in place to form a V. Black gains great power locally, this way. Therefore the point 1 is the vital point here: if White takes it instead Black would start to worry about cutting points.
White should by all means play White 1 here.
Once White has played the bulge point, White 1 sets up the cuts at a or b, either of which may be a good tactic.