As far as is known, hyperspace has no real existence and there are almost as many types of hyperspace within fiction as there are authors. In all cases it is envisaged as a means of starships being able to get to the stars within the lifetimes of both those on the ships and back home. This is generally not explained away in the story - just acting as a black box.
One of the more interesting variations on the theme is the way it is implemented by David Weber in his Honor Harrington books. Mr Weber envisages his version of hyperspace as a series of bands of ever contracted spaces all mapping onto a point in real space; the higher the band, the tighter the space so the faster your apparent real space velocity. There are also areas within these spaces that are analogous to currents in Earth's oceans. This enables David Weber, not entirely by co-incidence, to have his starships acting in a similar fashion as the sailing ships of Nelson's times.
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