As you approach a black hole (before the event horizon), both time and space will gradually become increasingly distorted. In regards to space, what you would see is that, as you approached the black hole, it would gradually take up an increasingly large portion of your field of view. That's true of everything, in a small way; even a nickel looks larger as you approach it. But imagine this effect is magnified hugely by the dense gravity; the black hole isn't just "larger," but gradually all encompassing. If you were to turn around to look behind you, the rest of the universe would gradually become a tinier portion of your vision, until eventually (as you hit the event horizon), everything besides the black hole is just one tiny speck directly behind you. The black hole is everywhere else -- up, down, left, right, in front of you. This is space warping around and folding in on itself.
Time would also become warped; specifically, it would slow down. From your perspective, though, you don't slow down -- time for any individual person always seems to go the same speed -- so instead, you see everything else speed up. As you approach the black hole, let's imagine you're still looking behind you, back towards the rest of the universe. Time will gradually speed up, and as you actually hit the event horizon of the black hole, time would become almost infinitely fast; you'd see the galaxy behind you rapidly age, erupt in to supernovas, and then fade away in to nothingness. To you, this would just be a few seconds, but to the rest of the galaxy/universe, it will be billions of years.
Finally, you enter the black hole. At this point, the idea of "looking behind you" ceases to have any meaning. The space that you think of as "behind you" has become so warped by gravity that it also points... in to the black hole. In fact, every direction you look is towards the black hole. Every direction you move is towards the black hole. If you could look "outside," you'd see time speeding by at an infinite rate, and from your perspective, the next thing you know is the end of the universe.