its when you run the system/components at max capacity in order to "break them in" per se. after the manufacuring process, on a microscopic level, ther are many rough edges and adn things that need as much power as can safely be put through it as possible in order to fully open up all the pathways. think of it like getting all the air bubbles out of a water cooled system. the air bubbles dont exactly hurt performance, but if get rid of all of em you will be that much more efficient.
some people will say burn-in is a joke, that its not necessary. i do it. its helped the stability of my ram, hasnt hellped me on a higher cpu overclock tho.