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 real world
The process is more or less same with the real world. But they "eat" not only to break down the pathogen or any substances, they also killed the pathogen. Unlike in anime, white blood cells killing pathogen by eating them, not slashing/shooting the pathogen.