In act 4, what do Ophelia's songs imply?

Ophelia's songs are first and foremost a way of illustrating the extent of her descent into madness—and not just because she is breaking into song at socially inappropriate moments. A well-bred noblewoman like Ophelia would never in her right mind discuss the topics that Ophelia sings about, particularly in the terms that she does: it was simply not acceptable for young, unmarried women to talk so openly and even graphically (e.g., "by cock") about sex (4.5.66).
The content of Ophelia's songs is important in another respect too, though. Certain lines suggest a connection to her father Polonius's recent death; she says, for instance, that an unspecified "he" is "dead and gone" (4.5.34). On the other hand, the sexual references call to mind her relationship with Hamlet—particularly because they revolve around the betrayal of a woman by her lover. In the song, the man promises to marry his lover only to discard her once she has slept with him. While we can't say with certainty that Ophelia and Hamlet ever slept with one another, it's not hard to see why she might feel betrayed by him. He toys with her emotions throughout the play (e.g., saying he loves her and then immediately denying it in act 3, scene 1) and ultimately kills her father. Polonius, of course, also treats Ophelia badly, using her as a tool to test his theories about Hamlet's madness. In fact, there are moments when Ophelia seems to conflate the two men in her songs; the lines "Which bewept to the ground did not go / With true-love showers" could refer just as easily to her ill-fated romance with Hamlet as they do to her father (4.5.44-45). All in all, then, Ophelia's songs point to the role that male manipulation and abuse has played in her decline.