An electric arc is nothing but a visible plasma that occurs during the breaking of the current flowing conductor at a shorter distance. Example Lightning, welding machine, short circuit etc.

Let us taken a simple example Air blast circuit breaker is operating at 765kV, 1300 Amps. Suddenly the breaker got an instruction to open the contact. The breaker will start open the contact. As you know the current is nothing but a flow of electron. In our case, you are suddenly interrupting the flow of the current of 1300Amps. Hence the current tries to catch the contacts, during that time, it ionizes the surrounding air.

This ionized air act as a conducting path to the current. 聽since the current flow persist even after you opened the breaker contacts. Look at the image.

This current flow in the ionized air seems like visible plasma and it is called as Electric arc.

The best example for the electric arc is your tube light. Inside the tube light, there is an electrical arc is formed.