Any good videos to watch that are Warcraft 1 and 2 in movie form to get caught up before watching this?
You really don't have to know what happened in those games to enjoy WC3. The orcs invaded from an interdimensional portal in the first game and razed the Human kingdom to the south, Stormwind. In the second game, the Human kingdoms in the north, The Alliance of Lordaeron, defeat the Orcs, chase them back through the portal to their homeworld, and defeat them again there. The remaining Orcs on Azeroth (this world's Earth) have been placed in internment camps or are living in hiding.
Uther was a major playable character in those games, and now as an older man he's the mentor of Arthas, the Human campaign's main character.
WC1/WC2 had very minimal story and most of it was actually added after WC3 was written and WoW became popular.