The end point of a stage, where land gives way to a sheer drop leading to the lower blast zone. The ends of “soft” platforms don’t count as edges. For something to count as an edge, fighters must be able to ledge-hang off it. “Ledge” is a frequent edge synonym.
Much of the most interesting combat in Smash occurs at the edge. There’s a tug-of-war between fighters who’ve been hurled off the side and want to recover past the edge to safe ground, and temporary “kings of the hill” who’ve knocked opponents off and are edge-guarding, trying to prevent them from returning. See any entries starting with edge, ledge, and recovery.