I want to give you an answer you can understand. What you saw was an immune response in action.
Anyone reading this who knows inflammation and immune responses will agree this is not the most accurate explanation available. But you will get the idea in spite of the anthropomorphized answer.
The complexity of that operation is pretty large. It is part of inflammation. Which is usually an ongoing process, that for simplicity, has cells bursting and/or leaving behind attractant chemicals for some other buddies that act like vacuum cleaners. I think you were watching one of the cleaner cells ingest another cell that probably had been painted with an "eat me" chemical signal,
Chemotaxis means movement of a cell toward (or away from) a source of a chemical. Cells in an aqueous environment usually swim with flagella. This is one way they can move. There are others. The biochemistry of movement is not trivial. And not all suited for a for forums like PF.
At one end of the reference book spectrum there is a science comic:
Science Comics: Plagues: The Microscopic Battlefield
Part of: Science Comics (20 Books) | by Falynn Koch | Aug 29, 2017
A little further up the food chain:
How the Immune System Works (The How it Works Series)
Part of: The How it Works Series (4 Books) | by Lauren M. Sompayrac | Apr 15, 2019
College, a bit dated
The Immune System, 4th Edition
by Peter Parham | Oct 1, 2014
NIH has immunology study section for scientists and physicians:
Google for "nih immunology study sections" - there are lots of them
For world class animations showing movement based on biochemical processes at the protein level see:
https://www.microbe.tv/twiv/twiv-726/