To underestimate is to guess that something is worth less or is smaller than it really is. You might underestimate the size of a one-pound hamburger until you realize it's too big to fit in your stomach.
When you "estimate" you take a guess at something, and when you underestimate, your guess falls short or below. If you underestimate how much something costs, you might show up at a store without enough money, and if you underestimate the strength of an opponent who is small, you might find yourself on the ground wondering what hit you. Often when we "assume" something, we make a guess based on how things appear — that's one way to underestimate.