What do people mean when they say they have "swum the Tiber"?
The short answer
The Tiber is the river running through Rome, with St. Peter's on one side. Converts say they "swam the Tiber" to mean they crossed over to the Catholic side.
The Tiber is the river that runs through Rome, with St. Peter's on one side. Converts to the Catholic Church often say they "swam the Tiber" as a metaphor for having crossed over to the Catholic side.