Hello Alex
When configuring MPLS VPN, one of the features that allows this to function is BGP. iBGP is what is used to allow PE routers to share routes between them on the MPLS carrier network. iBGP simply means that BGP is configured between routers in the same AS.
Now the term MP-BGP can be used for both iBGP and eBGP, and it simply means that information about more than a single protocol is being exchanged using BGP. MP-BGP simply means that we are activating a particular functionality of BGP, which is necessary for MPLS VPN, in order to include information about multiple protocols. Specifically, MP-BGP allows the use of NLRIs which include information necessary for MPLS VPN to function.
So MP-BGP and iBGP are not mutually exclusive, but actually indicate a different aspect of the BGP protocol.
Because iBGP is being used to exchange routes between PE routers, the PE routers themselves must learn the routes of the customers they serve. Because the CE routers exist outside of the MPLS AS, the routes must be learned via eBGP. eBGP peerings are defined as BGP peering between routers in different Autonomous Systems. So eBGP is configured between PE and CE routers so that CE routes can be made known to the PE routers, and can thus be propagated throughout the MPLS network.
I hope this has been helpful!
Laz