If you're coming out of shooter franchises and havn't touched an RPG before then even the "streamlined" sense of Skyrim may still be alien to you. They are going to be referring to events in Morrowind, Daggerfall, Arena, and Oblivion quite a lot (I assume)
You should buy Oblivion and/or Morrowind and play those. If you're interested and have the time download Daggerfall.
They're separating this game from the last one by 200 game years, it will seem new to all of us. There will be interesting things in the books and perhaps a few good references to the old games, but nothing to the point that you'd have needed to play all the games.
Separation aside you're still going to hear about the Oblivion crisis, The Tribunal, maybe the warp in the West, Ngasta, etc.
Every game lets any newbie jump in and test their tongue to see if the taste of the game suits them or not. play what you want, you won't be missing anything of the previous genre unless you yourself go and try them out.
That's not true, oblivion was my first TES game and when I first played I didnt know what the heck was going on. If you're interested in the story then it's definitely worthwhile playing the previous title.