When you say that the river is teeming with fish, what you mean is that the river is full of fish.* “In other words, `teeming with’ means in great numbers. It also means that the people or animals are moving around quite a bit.
Examples: ” I’m told that during summer, most hill stations are usually teeming with tourists.”
“It is also possible to use the expression `teem with’ figuratively. For example, Sujatha says her mind is teeming with ideas.”