A normal switch has two wires – input and output. It also has two positions – on and off. Setting it to the on position connects the input and output, closing the circuit, and the off position disconnects them, opening the circuit.
A three-way switch has three wires – one input and two outputs, A and B (or one output and two inputs, if you reverse it). The switch’s position determines whether the input is connected to A or B. Take two three-way switches and connect their A’s and their B’s. Now, if both switches are in the same position, the circuit is closed, and if they’re in different positions the circuit is open.
A four-way has four wires – two inputs and two outputs. The switch determines which input is connected to which output. Now, you take two 3-way switches and one 4-way switch, and connect one 3-way switch’s A & B to the 4-way switch’s inputs, and the other 3-way switch’s A & B to the 4-way switch’s output. Now, each change of the switches will open or close the circuit.
[This Wikipedia page](https://en.wikipedia.org/wiki/Multiway_switching) has diagrams to demonstrate.
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