Hi,
Usually they are used at the input stage. They can be needed in the output stage when the device can both sink and source current. eg In SG3524, it can either sink or source current, but can not do both, so you need to connect pull-ups or pull-downs at the output.
But usually, they are used at the input stage. Let's take an example. Say you have a microcontroller pin connected to a switch which is in turn connected to +5V. When the switch is closed, the pin receives +5v. However if the switch is open, the switch receives no input, it's not high or low, it's just a high-impedance (high-Z) input state, which can not be made use of in the code. So, you connect a pull-down resistor from the pin to ground, so that when the switch is open, the microcontroller pin is 0 - connected to ground.
Other applications maybe in communication, eg. I2C, etc, or converters, eg. ADC, DAC, etc.
Hope this helps.
Tahmid.
---------- Post added at 11:57 ---------- Previous post was at 11:44 ----------
The switch can source current when closed, but cannot sink current when opened. That's why the pull-down is required. Pull ups are required for the same reason as I explained with the SG3524 example.