Liches, as c-raven said, are extremely powerful mages who have the willpower for their soul to remain in the physical world after death. However, he failed to mention the fact that these mages were mostly evil, the good mages mostly passed on without a struggle, although some were arrogant enough to believe everyone else made a mistake and they could keep their minds (cheers for that Nekojin).
Apart from that, liches were incredibly powerful undead creatures, their magical abilities only enhanced after their ressurection. They have the power of necromancy and can raise the dead at will. They could quickly raise ghosts, skeletons and zombies at will, and could command the more powerful wraiths and banshees. Apart from necromancy, liches could also cast all the spells they knew before death, only with much greater power.