Dark energy is the name given to the force that is believed to be making the universe larger. Distant galaxies appear to be moving away from us at high speed: the idea is that the universe is getting bigger and has been since the Big Bang. Measurements are now accurate enough to allow astronomers to tell that these galaxies seem to be accelerating away from us. The universe is expanding at an increasing rate.
This faster and faster expansion is not understood by scientists. There are many ideas for what might be causing the rapid expansion. However, at the moment, cosmologists who study it do not have an answer. It is as if there was something there in empty space providing a repulsive force (Anti-gravity) that makes the universe expand. This has been named dark energy.
The following reference, which is beyond what can be discussed on this wiki, sets out the problem for theoretical physics.