ER = EPR is a conjecture in physics stating that two entangled particles (a so-called Einstein–Podolsky–Rosen or EPR pair) are connected by a wormhole (or Einstein–Rosen bridge) and may be a basis for unifying general relativity and quantum mechanics into a theory of everything.
The conjecture was proposed by Leonard Susskind and Juan Maldacena in 2013. They proposed that a non-traversable wormhole (Einstein–Rosen bridge or ER bridge) is equivalent to a pair of maximally entangled black holes. EPR refers to quantum entanglement (EPR paradox).
The symbol is derived from the first letters of the surnames of authors who wrote the first paper on wormholes (Albert Einstein and Nathan Rosen) and the first paper on entanglement (Einstein, Boris Podolsky and Rosen). The two papers were published in 1935, but the authors did not claim any connection between the concepts.
This is a conjectured resolution to the AMPS firewall paradox. Whether or not there is a firewall depends upon what is thrown into the other distant black hole. However, as the firewall lies inside the event horizon, no external superluminal signalling would be possible.
This conjecture is an extrapolation of the observation by Mark Van Raamsdonk that a maximally extended AdS-Schwarzschild black hole, which is a non-traversable wormhole, is dual to a pair of maximally entangled thermal conformal field theories via the AdS/CFT correspondence.
Susskind and Maldacena envisioned gathering up all the Hawking particles and smushing them together until they collapse into a black hole. That black hole would be entangled, and thus connected via wormhole, with the original black hole. That trick transformed a confusing mess of Hawking particles—paradoxically entangled with both a black hole and each other—into two black holes connected by a wormhole. Entanglement overload is averted, and the firewall problem goes away.— Andrew Grant, "Entanglement: Gravity's long-distance connection", Science News 
This conjecture sits uncomfortably with the linearity of quantum mechanics. An entangled state is a linear superposition of separable states. Presumably, separable states are not connected by any wormholes, but yet a superposition of such states is connected by a wormhole.
The authors pushed this conjecture even further by claiming any entangled pair of particles—even particles not ordinarily considered to be black holes, and pairs of particles with different masses or spin, or with charges which aren't opposite—are connected by Planck scale wormholes.
If we believe in the ambitious form of ER = EPR, this implies the presence of an Einstein–Rosen bridge connecting the superposed wave packets for a single particle.
A related notion is the ER = EPR conjecture of Maldacena and Susskind, relating entanglement to wormholes. In some sense, we’re making this proposal a bit more specific, by giving a formula for distance as a function of entanglement.