"Whimper" is an old word that someone probably made up because it sounds like someone whining and crying at the same time, like this: "Whimp, whimp, whimp."
A whimper is a sad little quiet sound of whining and crying.
When you whimper, or when you whimper something, you’re making quiet little sad noises, or you're saying something in a quiet, whiny way.
You might whimper if you just stubbed your toe. Your dog might whimper if he wants you to look at him and play with him. And sometimes, when it's early in the morning, and time for me to get up, I whimper, "Nooo, I wanna sleep more!"