Swarming just refers to the fact that multiple people work together to complete a task or story. In my experience this isn't something you do often.
Typically, each member of my team works on a different task and/or different story. If someone is falling behind, or if there's a desire to finish a task or story early, other people will stop working on other tasks and "swarm" to complete the task, which means they all work together on a single task or story until it is completed.
We recently had a small number of stories that was some fairly boring, uninteresting work. I gave the team a small incentive (pizza) and deadline (end of the day) to finish the work, so they swarmed on the story and knocked out at least a couple days of work in one afternoon. They got the work done and out of the way early, then each team member went back to whatever they were working on. They got a free lunch, I got work done early that could have dragged on due to it's dull nature, and the team got ahead of their sprint. Win-win-win.
"Swarming" is nothing more than a fancy term for "hey, let us help you with that".