The concept of dark energy gives explanation to the observed accelerating expansion of the universe, which otherwise would be decelerating. Dark energy can be inserted into general relativity's field equation in the manner of the cosmological constant that Einstein originally included to maintain the universe's size. With dark energy, such a term is theorized to be sufficiently large to increase the size of the universe, and it isn't clear that it is constant.
The acceleration of the universe's expansion is evidenced by the geometry of viewable space, both from the frequency of supernovae and in the cosmic microwave background. The supernova evidence dates from the late 1990s and since then, the CMB's suggestion of a flat universe has been interpreted as evidence. The concept is very well accepted.
Alternatives to the dark energy hypothesis would be other adjustments to general relativity (e.g., DGP gravity), or that it is an illusion, e.g., its evidence stemming from selection bias.
An energy explanation of the accelerating expansion would be explained by some kind of vacuum energy, i.e., present even in a vacuum, thus the term dark energy. An obvious candidate is zero-point energy predicted by quantum theory but the measured acceleration of the universe's expansion requires a vacuum energy sixty orders of magnitude smaller than this theoretical zero-point energy, a situation which has been cited as and extremely large gap between theory and measurement.