To handle something is to control it, the way an elephant handler might handle an elephant, or the way you would use a handle to lift a suitcase. If you're panicking, a friend might suggest you "get a handle on yourself."
How to get a handle on the word handle? Start with the thumb. Much like the word “thimble” is derived from “thumb,” “handle” essentially refers to an object held "in hand," or placed under your control. Handle can also have a more abstract meaning, such as understanding or grasping a concept. You should be able to handle geometry before you start trig, right? A handle is also slang for a nickname. "What's your handle?" is another way of saying "What's your name?