The Alcubierre drive is an idea for a faster-than-light spaceship. It works by contracting space-time in front of the ship, and expanding it behind the ship. Physicists say that this requires the use of negative energy or exotic matter. But why is that? I mean, positive mass and normal gravitational fields do bend space-time. If we could get a hold on creating and manipulating large gravitational fields, wouldn't we be able to create this drive?
Bending spacetime is not enough, you will also need to do it in specific ways. The simplest way of visualising the difference is to look at the Raychaudhuri equation, which describes how masses move in a gravitational field. If a gravitational field is generated using only positive energy (more precisely, obeying the weak energy condition), gravity is always attractive. If you allow negative energy, you can get bodies originally converging to a point suddenly diverging.
In the case of the Alcubierre drive, you need to both expand the space behind you and contract the spacetime in front of you (although the Alcubierre metric actually requires negative energy EVERYWHERE, but I'm not exactly sure how to work this out).