When you forget something, you can't recall or remember it. An actor who forgets his lines might need some helpful cues from the other actors on stage.
You might forget on online password, or forget to return your library books. You can also deliberately forget something: "I've decided to forget about becoming rich and famous and focus on what I like to do." When you accidentally leave something behind, like your umbrella, you also forget it. The Old English root of forget is forgietan, "fail to remember or neglect inadvertently."