what does pull-up resistor and pull-down resistor mean? How do I implement them in my circuit?
It's very simple:

A pull-up resistor pulls the voltage up to the "high" logical level (5V, 3.3V or whatever is used as a "high" level) when the is no signal driving the input.

A pull-down resistor pulls the voltage down to the "low" logical level (0V or close to it) when the is no signal driving the input.

This is achieved because the input impedance of the device being pulled up/down is usually very high (and much higher than the resistor itself, so they won't form a voltage divider). Due to this there is almost no flow of current through the resistor, and the voltage drop is almost zero volts. This means, in turn, that the voltage (either "high" or "low") you are connecting the resistor to then gets passed "as is" to the input of the device being pulled up/down, which helps set a "default" input value when there is no signal driving it.

However, when an input signal appears, it will usually have a source impedance much lower that the pull up/down resistor, and will dominate he combination and set the state regardless of the resistor.

This diagram (source here) illustrates the behaviour described:



EDIT:

Regarding your specific use case, you'll need to pull down the input of the BJT. Use a resistor 20x R1 and it'll probably be fine.