About 68.3% of the universe is made of dark energy, according to current calculations. It is baffling that we know so little about it. The rest of the universe is made of dark matter (26.8%) and "normal" matter (4.9%). It is called dark energy, because we aren't able to see or measure it.
Probably the first question that pops up in your head is how do we even know it exists. Well, "know" might not be the best word, but by observing how the universe is expanding, we can expect that it does. The universe is not only expanding, it does so at an accelerating rate. If there was no dark energy, the explicitly attractive gravitational force would have slowed the universe's expansion. Since this is not the case, as Hubble Space Telescope observed in 1998, there had to be something that forced the universe to expand at accelerated rate.
There are couple of solutions as to what this dark energy could be. Einstein realized that empty space is not nothing. It has properties. It is possible for more space to come into existence. Furthermore, Einstein predicted that "empty" space can have its own energy. He predicted this in the version of the theory on general relativity where he introduced cosmological constant. We don't understand why the cosmological constant should be there. It is a mathematical representation of the value of energy density of the "empty" space. Einstein later removed it from the theory, only for it to be reintroduced after the dark energy was introduced. As more space comes to exist, the energy is not diluted, because it would appear together with space. This makes the universe expand faster and faster. Also, this means that with time, universe has more and more dark energy.
Other possible explanation comes from quantum theory. Quantum theory sees empty space as not-so-empty, but a space filled with temporary, virtual, particles. Imagine particle and antiparticle appearing for the fraction of the second and then annihilating one another. That's what matter and antimatter do when they collide. But when physicists tried to calculate how much energy this would give empty space, the results were so off, they were dismissed.
Dark energy could also be something theorists call quintessence – some sort of dynamical energy fluid or field that we can't detect. Finally, Einstein's general relativity theory could be wrong and new theory would have to explain the accelerated expansion of the universe while also maintaining or improving the way general relativity theory explains the movement of planets, stars and galaxies.