A two-timer is the person who does the two-timing: someone who keeps a secret second relationship going while already with a partner. It is a noun and an insult, but a light, almost comic one — the sort of thing said with a slap on the arm or across a bar, not the word you would use about a real betrayal that has broken someone's heart. For that, English says 'he cheated on her' and leaves the name-calling alone. It sounds dated, the way old films sound dated; a young person today would more likely say 'he's a cheater' or just 'he cheated'. Because of that datedness it turns up a lot in song titles and headlines, where the slightly old-fashioned ring is the point. Note it describes a pattern of behaviour, not one mistake — calling someone a two-timer says this is who they are. As with the verb, keep it away from the other 'two-time': 'a two-time champion' is a person who won twice, and 'two-timer' never means that.