Necron Lords used to be actual lords, back when the Necrons were still fleshy and called Necrontyr. Presently, each Lord rules over a single Tomb World and all of its legions and phalanxes, assisted by a court of lesser nobles, and is himself a part of an Overlord's Royal Court (along with the Lords of neighboring Tomb Worlds and a few Crypteks as well). Because they were nobles, they were given higher-quality bodies and their minds were left quite intact by the biotransference, and so they are free-willed individuals, with names and personalities. That said, the millennia in stasis have done strange things to their minds, to say the least.
The Necron Lord used to be the only customizable HQ choice available to the Necrons (the non-customizable HQ choices being the Deceiver and the Nightbringer), but was otherwise devoid of character (to the point that, in Dawn of War: Dark Crusade, the "voice" of the Necrons was a Pariah). With the infusion of character brought by the Fifth Edition Codex, Lords are now individuals in their own right (with names and everything), but with the new layers of rulers above them, they are not available on their own anymore; instead, you get up to five of them as a "Royal Court" for each Overlord in your army, and can parcel them out to lead a squad of Warriors, Immortals, Deathmarks, or Lychguard, rather like a Sergeant or Wolf Guard.
The 7e updated codex brought them back as a HQ choice in their own right, though.
When the Necrons were first introduced in Second Edition, the Necron Lord miniature was a scowling skele-bot with a goofy headdress (not that the other Necron miniatures were less silly). The miniature was later updated to be sleeker and have more options, though the old design was kept around as the "Classic Necron Lord" and updated to Finecast when the new Codex came out. It is now no longer available.
- Necron Lord of All Kaurava, an ancient (even by Necron standards) lord who want those fucking kids to shut up.
- Assholetep the Insufferable, a tantrum-prone Classic Necron Lord.