VRF (Virtual routing and forwarding) is a technology that allows multiple instances of a routing table to co-exist within the same router at the same time. Overlapping IP addresses can be used without conflicting with each other as the routing instances are independent. The multiple Routing instances can be made to travel across different paths (i.e. take different outgoing interfaces).
VRFs are the same methods of network isolation/virtualization as VLANs. VLANs are used at the L2 and VRFs are L3 tools. VRFs are to routing table like VLANs are to LANs.
Related – VDC vs VRF