Austrian physicist Ludwig Flamm (1885-1964) inspired by Albert Einstein's publication of his General Theory of Relativity in 1915, realized that the solution to Einstein's field equations described a Black Hole, and that another set of solutions described what Flamm termed a "White" Hole. He further realized that these two "holes" were mathematically connected by a space-time conduit, and that anything entering the Black Hole could exit through the White Hole. The space-time tunnels between the holes became known as "wormholes." In theory, travelling through a wormhole would be faster than light travel, because it would be nearly instantaneous from one end to the other. The wormhole connects different areas of space that could be millions of light years apart, or even space in a different universe.
However, no one's ever yet made this journey. Scientists have measured some of the properties of Black and White holes, and although they have not been detected, the theory implies that wormholes do indeed exist.
Numerous submicroscopic quantum wormholes are believed to exist in every cubic meter of space.
Macroscopic wormholes are not generally believed to exist unless the dark energy that's accelerating the expansion of the universe is a form of "negative-energy" matter.
Macroscopic wormholes are theoretically possible without negative-energy matter, if Einstein's theory of gravity (general relativity) is inaccurate at very high curvatures of spacetime. In this case, Einstein's gravity would have to morph into what's known as "Gauss Bonnet gravity" or "Lovelock gravity".
Wormholes have never been observed.