Buck and Boost normally refer to the operation of a switchmode power supply. Though it may also be something else, but I will stick with what I know, the operation of switchmodes.
Lets start with BOOST since it is the easiest to understand.
You may have played with a large coil and a car battery.
You connect the coil across the terminals and nothing much appears to happen, but when you take the coil off you receive one hell of a jolt from the Back EMF.
The coil is like the flywheel in an engine. When you pass current through a coil, it builds up a magnetic field. When you disconnect the power, the coil wants to keep the amount of current flowing. It will build up a tremendous voltage trying to do it as the magnetic field breaks down.
So our switchmode circuit consists of a transistor in series with an inductor between +VDC and Earth. Lets say the 12V car battery. At the positive terminal of the coil is a doide in series with a capacitor to earth.
We switch on the transistor and current flows in the coil.
Now we switch off the transistor and the back EMF is created in the coil, this flows through the diode and charges the capacitor. The voltage across this capacitor quickly builds up to something much greater than the source voltage.
We sample this voltage and adjust the switching of the voltage to regulate the higher output voltage.
So a boost circuit takes a small DC voltage and boosts it up to a higher voltage. The output voltage is always higher.
A BUCK converter is the opposite. The output voltage is always lower (but with more current).
In the buck converter, the inductor and diode are swapped around in the circuit. Now we turn the transistor on and current starts to flow through the inductor from the much higher voltage source. But the voltage is not instantly on at the output, instead it takes time to rise. When the correct voltage is obtained across the capacitor the transistor switches off. The coil will now continue to maintane the same amount of current to the capacitor and load with the reutrn curent path through the diode.
But the coil cannot provide this current indefinitely and eventually the voltage across the capacitor will drop where one again we turn on the transistor in a very short pulse to push the coil's current once again.
A BUCKBOOST converter is a hybrid of both.
The output voltage can be either higher voltage or higher current than the input source.
If we take the same circuit as the boost converter, but reverse the diode polarity, we find that when we turn on the transistor we 'spin up' the inductor as before, but now turning the transistor off effectively switches the load into circuit.
The output voltage can be made eithe higher or lower than the input voltage by adjusting the duration of the switching.
The output voltage of a buckboost converter is always reversed from that of the source voltage.
The are most often used to generate negative power rails from a single positive rail supply.