What is the difference between ibgp and ebgp and when do we use ebgp and ibgp? Explain that.

Very simply, eBGP is used for inter-AS routing, where as iBGP is used in intra-AS routing.  Everything else in every other answer is detail surrounding this core difference.

Now; it is not quite accurate that a BGP session between2 BGP routers is an eBGP session - one counter example scenario is connecting a customer to an ISP, whether or not that customer has an own AS number; eBGP doesn't need to run between the customer's border BGP router and the ISP's.

In short

• iBGP is BGP used internally to exchange BGP information between multiple BGP border routers.
• Routers speaking iBGP must be connected in a full mesh to prevent loops.
• If reflectors or confederations are used, the iBGP mesh may have convergence issues that can cause blackholes, that's when static route injection becomes useful.

ibgp is "internal". It is commonly used to distribute external routes inside your AS

ebgp is the only one protocol to send routes (both internal and external, depends on requirements) to another AS.

A BGP Session between two BGP routers that are in the same Autonomous System is called iBGP while a BGP session between 2 BGP routers that are in different Autonomous System is called eBGP.