What is a Einstein-Rosen Bridge and what does it have to do with space?

Answer 1

It's a so called wormhole.

A wormhole is a theoretical solution (kruskal solution) of equation coming from the general theory of relativity (the theory Albert Einstein was describing space and time with).

One of the predictions of this theory also leads to the effect of wormholes, not described by Einstein himself from his theory but based on his equations and in cooperation with another scientist called Nathan Rosen (in 1935).
Therefore, the initial name for "wormhole" was Einstein-Rosen-Bridge
"bridge" because it is presumed to connect two distand areas in the space-time as like as a bridge connect two opposite river banks.

However, from nowadays string theories we still kinda predict the existence of wormholes, but by the conatining maths and physics, these would be very different from the postulation of the "Einstein-Rosen-Bridge".