What is VRF and why do we configure a VRF in BGP and OSPF?

VRF stands for virtual routing and forwarding. it will creat a separate routing table in the same device. just for understanding, we can say it is like VLAN. VLANs are on layer2 but VRF is on layer3. it is usually used for MPLS L3 VPNs and it allow the reuse of IPs.

In MPLS, VRF means virtual routing forwarding. It is separate routing table apart from global routing table in PE router. Each customer connected to PE have different VRF table

VRF stand for Virtual Routing and Forwarding. VRF is a separate routing table for individual customer. VRF is created by giving a unique name and separate from the global routing table.Its mainly used for security purpose, Its make the customer routing table simple and easy to troubleshoot.It is used MPLS VPN topology.