A technique which is used in non-custom games on Battle.net. The players involved will immedietly build up their base as fast as possible, focusing on acquiring a hero and 3-6 low level units for a "rush" attack. Most commonly executed within the first 5-10 minutes of the game, the rush-ees will attack a certain base, focusing on units harvesting wood or gold, or in rarer cases, the main building. A successful rush can very easily render the victim useless, therefore giving the attackers a instant and strong advantage.
Alternatively, a person controlling the Orcish race can obtain a Blademaster and harass. His primary attribute is Windwalk which allows him to become invisible and on breaking invisibility, doing extra damage to the victim in subject (this is similar to a rush in some aspects, mainly targeting workers harvesting resources or buildings in low levels of completion). When done properly, a blademaster harass can completely put the victim out of sync and low on resources, which consequently may lead them to play a poor game or leave the game entirely.
Dude 1: "HAHAHA OMFG u guys totallyy got rushed, look ur so dead nub. wat an awsum hero rush. gg LOL!!!!!!!!11"
Dude 2: "Uhh, you killed one peon dumb ass."
Dude 1: "stfu".
In Warcraft III (Reign of Chaos or The Frozen Throne), the practice of attacking the opponents base using only your hero (and any summoned units, if the hero is a summoner of some kind). Mostly prevalent in multiplayer games when there are multiple allies, thus maximizing the effect. In a Hero Rush, the opponent's workers are usually targeted first. The purpose of a hero rush is to strike early to gain a huge (and hopefully insurmountable) advantage.
Red and Pink are doing a Hero Rush on Teal. TP (teleport/town portal) to Teal now.