EEVEE is a GPU based realtime engine for the viewport implemented for Blender version 2.8, using industry standard PBR (physically based rendering).
The EEVEE engine will be a PBR realtime engine for Blender 2.8 viewport aimed at replacing the Blender internal render engine.
From the Eevee Roadmap:
Eevee will follow the (game) industry PBR (physically based rendering) trend, supporting high-end graphics coupled with a responsive real time viewport.
Some of the main features:
Support for all realistic Blender light types
PBR materials with Ubershaders similar to those used in game engines
Image based lighting
Glossy rough shaders
Post process effects, like motion blur, bloom, tone map, depth of field, and ground truth ambient occlusion
Environmental map arrays
More information is on EEVEE (Blender wiki).