To soft-boil an egg is to cook it in its shell in boiling water just long enough that the white sets fully while the yolk stays runny. Timing is the whole technique: roughly 5 to 7 minutes in already-boiling water, depending on egg size and how set you want the yolk, versus 9 to 12 minutes for a firm hard-boiled yolk.
Soft-boiled eggs are typically served in an egg cup with the top sliced off, so the yolk can be scooped out with a spoon or dipped into with strips of toast ("soldiers") - a classic part of a traditional English breakfast. The runny yolk also works as a dip for bread or crackers, or spooned over rice, noodles, or vegetables as a quick sauce.
Soft-boiled differs from poached, where the egg cooks out of its shell directly in water, and from coddled, which cooks the egg gently in a covered dish rather than a full boil.