TIG, tungsten Inert Gas, GTAW, Gas Tungsten Arc Welding, same things. It mean you use an electric arc torch with a nearly non-consumable electrode to produce a weld pool. You can either fuse the material by melting the two base metals into each other or by using a filler rod. The beauty lies in the fact that since the electrode isn't deposited into the pool (unlike MIG or Stick) you can weld damn near anything with little to zero contamination of the weld pool. This is particularly nice when welding touchy materials like Ti, Al, Mg, CrMo (which can also MIG'd with varying degrees of success).
The weld pool is also infinitely variable in depth, unlike MIG and stick. So you can control depth of penetration pretty easily.