A pull-up resistor is a resistor connected between a signal line and a positive voltage supply. It keeps the signal at a high logic level when nothing else is actively pulling it low.
Why pull-up resistors are used
Digital inputs can float if they are left disconnected, which means the circuit may read random high or low values. A pull-up resistor gives the input a stable default state.
Where pull-ups appear
Pull-up resistors are common with buttons, switches, open-drain outputs, I2C communication, and microcontroller input pins. Some microcontrollers also have internal pull-up resistors.
The key idea is simple: a pull-up resistor gives a signal a default high value without forcing it permanently high.