Is this homework?what is the function and operation of this circuit? Is it a two way two lamp circuit?
It might be in the USA, but in the UK (at least) it's called a 2-way switchThis is called a 3-way switch.
There's not universal agreement on this, also there's some subtlety. The physical switches used are often called "3-way switches" (presumably because there are three terminals), but the circuit itself is often called a "2-way circuit" (but "3-way circuit" is also commonly used, possibly because it's a circuit that uses 3-way switches).Welcome to AAC!
This is called a 3-way switch.
It is used for controlling a lamp from two distant locations and is required by building codes for lights illuminating a long passageway, hallway, or a flight of stairs.