Well now that's a big question!
Route redistribution is where a router takes routes in from one routing protocol (loosely defined) and advertises them via another routing protocol. Most networks gravitate toward a single routing protocol, but border routers that interface with other networks may need to speak a separate routing protocol. E.g., if I run my network with OSPF as my IGP, but peer with my provider using BGP, I may need to redistribute routes into OSPF that I learn from my provider or redistribute routes that I learn on my IGP into BGP.