Steering and flocking
Also said as Boids, Steering behaviours, Separation, alignment, cohesion
Each creature follows simple local rules for its next movement. Craig Reynolds showed in 1987 that three are enough for a flock: keep apart, match your neighbours' heading, drift to their centre.
You cannot hand-animate a thousand birds, and no one thing has to be in charge. It looks alive because it is not planned. Its weakness is that a flock can't solve a maze, which is pathfinding's job.
Say it
“For the swarm, use boids with separation 1.5, alignment 1 and cohesion 1, and a seek force towards the player, so they surround you without any shared plan.”
Where you’ve seen it
Reynolds' boids reached feature films in Batman Returns in 1992, as its swarms of bats and its army of penguins.
Not to be confused with pathfinding
Flocking only knows about the neighbours in reach. Pathfinding knows the map. Crowds often use a path for where to go, and steering for how to get along on the way.