Answer
DIAPEDESIS is the process by which WHITE BLOOD CELLS squeeze out through the walls of intact blood capillaries into the surrounding tissues, in order to reach the site of an infection.
The word means "leaping through". White cells are AMOEBOID — they can change shape and put out pseudopodia — which allows them to force their way between the cells of a capillary wall without damaging it.
WHY IT MATTERS: bacteria do not enter the bloodstream to be attacked; they multiply in the tissues. So the defending cells must LEAVE the blood to reach them. Diapedesis is what makes that possible, and it is the reason an infected area becomes swollen and full of pus — pus is largely dead white cells and the bacteria they engulfed.
Note that RED cells cannot do this; they have no nucleus and cannot change shape in this way, so they remain inside the vessels.