In the United States, a title establishes a vehicle's ownership.
Every vehicle has one (and only one) title at a time. When a person or dealership sells a vehicle, the seller provides the vehicle and the title to the buyer.
When the buyer receives a vehicle's title, he or she submits it to his or her local vehicle registration authority as part of the registration process.
The buyer's local registration authority issues a new title, bearing the vehicle's details and the new owner's name and address, usually with a few days or weeks.
This process of submitting a title to the authorities ensures that every vehicle has one (and only one) title at a time, and helps ensure that a vehicle owner can only sell a vehicle once.
Titles establish vehicle ownership, not the right to drive the vehicle on public roads
Registration, which is a separate document from the title in the US, permits a vehicle's operation on public roads.
This differs from many countries, whose ownership and registration documents are one and the same (v5c in the UK, the Rego in Australia, etc.).
The States, not the federal government, are responsible for vehicle administration, including titles.
Each of the 50 United States, plus Washington, D.C., issue titles in their own format.
Every State (plus D.C.) recognizes the titles of every other State (plus D.C.), so it's not difficult to register a vehicle in one State that was bought in another State. It's common for a car to have been titled to many States throughout its life.
Example of a California vehicle title