NO and NC contacts are standard set of contacts available with an electromechanical relay. NO contacts are open in normal condition. When the relay coil is energized, NO contacts are closed.
NC contacts are closed in normal conditions. When the relay coil is energized, NC contacts are opened.
NO and NC contacts are most commonly used symbols in PLC ladder logic or any industrial control circuit to indicate digital input. They are derived from relay contacts. The input can be switch closure, push button closure etc.
1) Physical NO/NC contacts are used in relay based control circuits
2) Relay equivalent of NO/NC contacts are used in all ladder diagrams.