A pullup resistor will be found connected between some signal and v+.
A pulldown resistor will be found connected between some signal and signal_ground(0V).
Common uses are where an input to some component requires one of two voltage states to operate reliably but you are driving the input with some component that can only drive a signal in one way.
Maybe the input is the gate of a FET, maybe an input to a microcontroller or a logic gate.
Maybe the output is coming from an open drain fet or an open collector BJT transistor or maybe you have a situation where many outputs got diode or'ed.
The deal is that the input can deal with the driven signal from the output but when that signal is no longer present, there's a good chance that you now have a situation where the input sees high impedance. Under these circumstances, what signal the input "sees" is unpredictable. It could pick up noise from nearby electrical cables. It could pick up static electricty discharges from nearby etc. The input may end up switching states at undesirable frequencies. Of course usually you don't want the input to be able to "switch" on its own at all. So you pull the signal up or down when the opposite driven signal is idle.
The value of a pull resistor depends on your power budget, the max current/voltage/power the output components can deliver and what voltage/current the input requires to see a steady state that is opposite to the "driven" output state.