Inside a potentiometer there is a conductive track (usually carbon), and either end of this track is connected to the two outer connections of the pot. The middle connection is a wiper which is mechanically connected to the shaft, so as you rotate the pot, the wiper gets closer to one end of the track, and further from the other. As the track has a resistance (the stated resistance being that of the total track; ie, from one end to the other), as you move the wiper, the resistance from the 1st connection to the wiper and from the wiper to the 3rd connection, changes.
In the diagram above, the volume pot is wired as what is known as a 'potential divider'-- it divides the potential ('potential', being voltage) between the output at the wiper and at the end of the track. So if the wiper is closer to the 1st connection (on the left, where the output of the pickup is wired to), then the full signal will take the path of least resistance, and go to the output jack. As you wind the pot down, the signal is divided between the wiper and the last contact (ground), so your signal output gets lower, as a portion of the input signal has been sent to ground, via the 3rd contact.
The tone pot is configured as a simple variable resistor (note, the unconnected lug of the pot) which, in conjunction with the cap, forms a filter which diverts some of the signal frequencies to ground.
Hope that answers your question!
(as a side note, the extra cost of higher quality pots gives you a better laid track (sometimes a different material, such as plastic-carbon, or conductive plastic), which will last longer (the friction of the wiper on the track will cause the track to wear out over time). Also the tolerances and taper of the track are likely to be higher, and the build quality should be better (the movement of the shaft should be smoother and less scratchy).
