On our circuit breaker, we have several circuits that are linked together by a metal handle. For instance, there are several cases of three 20A circuits all linked together, meaning you can only flip all three at once. Does that mean those three 20A circuits equal 60A? If not, what is the purpose of having multiple circuits linked together?
Each circuit is rated 20 amperes.
Handles are typically tied together when all the breakers are supplying a single piece of equipment. For example, in a 120/240 volt single phase system, two breakers might be tied together for a piece of equipment that requires 240 volts. Three breakers tied together would be common for a 3 phase systems.
In all situations, the circuits are still rated whatever is listed on the handle, not the total of the breakers.
There are several reasons for having two-pole breakers, or handle-tied breakers. 240V circuits or multi-wire branch circuits (shared neutral) both require two-pole breakers.
The amperage of a breaker is what's on the handle. You DO NOT add up the numbers. A single pole 20A breaker is (for residential in the US at least) a 20A/120V breaker. A two-pole 20A breaker is a 20A/240V breaker.