VRF (virtual routing and forwarding) is a core technology of MPLS which allows a service provider to provide BGP routing to many customer VPNs while isolating each customer's routing tables.
VRF lite provides the same isolation in an enterprise LAN.
Imagine you have a corporate LAN with a number of VLANs and a default gateway to the corporate WAN.
If you want to add a guest VLAN with a default gateway to the internet, you can simply exclude it from the corporate LAN by not providing a switched virtual interface (interface Vlan on Cisco) on the guest VLAN.
Now suppose you need a second guest VLAN and you need to route between the two guest VLANs and the Internet without opening a hole to the corporate LAN.
This is a use case for VRF lite. On each layer 3 switch or router, you create a VRF for the corporate LAN and a VRF for the guest LAN. You map the VLANs to the appropriate VRFs. There are now two separate routing tables and no traffic can pass between them (unless you specifically configure that).