Phagocytosis

 is one of white blood cell's main skill. So they are able to pass through capillary walls in order to get wherever they need to go in the body.

Comparison With The Real World
The process is the same more or less in the real world, but they "eat" not only to break down the pathogen or any substances, but also to kill the pathogen. Unlike the white blood cells in Cells at Work, white blood cells in real life kill pathogens by eating them, not slashing/shooting them.