Once you've destroyed all three Inhibitors in a lane, your team will spawn 'Super Minions' in that lane, which are significantly stronger than regular minions. These Super Minions are excellent for pushing down the remaining turrets and the Nexus. After winning a decisive team fight, especially with Baron or Elder Dragon buff, group up and push directly for the enemy Nexus. Focus fire on the Nexus, ignoring enemy champions unless they pose an immediate threat. The game ends when the enemy Nexus is destroyed.

The Nexus Push — League of Legends Walkthrough