The verb relate means "to make a connection." If you can relate to someone's story, something like that has happened to you.
Relate also means "to give an account of something verbally," like relating details of your trip to Sweden. That meaning of relate comes from the Latin word relatus, meaning "to recount, tell." If you talk about the federal budget crisis, people might not be interested until you relate it, meaning "explain the relationship between," to the possible job cuts at your local schools and police departments.