to swarm: to teem with dense, moving masses of small living creatures, or to breed and multiply in such swarming numbers
The word paints a single vivid picture: life so abundant that it moves in restless, crowded masses. It is the word for water "swarming" with fish, ground crawling with insects, a river turned thick with frogs. The emphasis falls not on any one creature but on the sheer, overflowing density of them.
From that picture the word naturally extends to rapid reproduction. When Genesis tells the animals leaving the ark to "breed abundantly," or describes Israel multiplying in Egypt until the land was full of them, it reaches for this same word. Teeming presence and prolific breeding are two sides of one idea: numbers multiplying past counting.
Two neighbors sharpen the sense. Where רָמַשׂ pictures the low, gliding movement of small creatures, this word stresses how many of them there are; and where רָבָה is plain increase in number and פָּרָה is bearing offspring, this word adds the image of a swarm, increase you can watch churning and spreading across a place. The creatures it describes are named by the matching noun שֶׁרֶץ, the "swarming things."