Wormholes are hypothetical entities that show up in theoretical analyses of Einstein's theory of gravity (general relativity). Nobody has yet seen a wormhole, nor are we certain that they exist, but they seem to show up so easily when we do calculations that many physicists suspect that they might actually be out there in the real universe."

Source : Scientific American (quote from Professor Matt Visser, School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, NZ)

The name 'Wormhole' was first suggested in a 1957 paper from American theoretical physicists John Archibald Wheeler and Charles Misner.

But the idea of a structure which could perhaps link vastly separated areas of the universe (or universes) at different points in time had been suggested much earlier. In 1935, for example, Albert Einstein and Nathan Rosen suggested in their paper 'The Particle Problem in the General Theory of Relativity' the possibility of a linking-structure which later became known as an Einstein–Rosen Bridge.

Since then, many cosmologists have provided theoretical (i.e. mathematical) workings which appear to show that wormholes could exist - not only 'connecting' parts of the universe billions of lightyears distant (as well as billions of years apart in time) but also providing 'shortcuts' to other 'universes'.

At present, however, there is no proof that such structures actually do exist.

It's worth noting that the opening paragraph of the 1935 Einstein - Rosen paper (linked above) read :

In spite of its great success in various fields, the present theoretical physics is still far from being able to provide a unified foundation on which the theoretical treatment of all phenomena could be based."