The best way to explain it is like... ok, you know grass pop-in on games? Well that grass isn't just pulled off the HDD/SSD... you have your surrounding area that is rendered, and then an increased area beyond that of data stored in VRAM waiting to be rendered. It's far faster than if the game just pulled it off the hard drive... Now when you run out of VRAM, you get horrible stutter, because the game is forced to pull new assets from the drive.
For now, 5 GB is the most you'd need. I saw a 4.5 GB draw for me on Watch Dogs, but that is the most I've ever seen. But like we saw with the 290x, a lot of people purchased that card to future proof themselves because... "when would we ever need 4GB of VRAM." We will only see more and more VRAM needed as games get more detailed and DX 12 comes out. I would say the Ti will not run into any problems in the near future at resolutions of less than 4K. At 4K, it could have a few problems on *some* games by the end of next year.
I would like to point out that VRAM will not give you more fps... It will only give you a smoother game play experience on games that would otherwise exhaust the VRAM on the other card. With that being said, the 980 Ti is far faster than the 980 regardless, and is a great buy.