A transponder in the physical sense is basically a radio. In terms of transponders in your signal strength menu, it refers to a specific band of frequencies. Think of a particular transponder in the same way as you think of a regular over the air TV station you'd pick up with your antenna.
Satellite companies are assigned their frequencies, or transponders, on a nationwide basis. Before the advent of spotbeams, satellites sent the same signal over the entire country. This meant that anything on any particular transponder would be received at any location in the country, and the signal would be exactly the same. This was fine when satellite TV was only delivering national TV channels and everyone was getting the same thing. As a matter of fact, it was hugely efficient and is why satellite had/has more channels on average than cable.
Several years ago satellite TV companies started carrying local channels. Due to copyright laws and contractual issues, only viewers in a local channel's home market can view those particular channels. However, due to the way that satellite technology works, those channels were being beamed to the entire country. It was very very inefficient. Now, that doesn't mean that viewers in NY could see LA TV stations. Using smart cards and conditional access they were/are able to block viewers from seeing out of market channels.
Engineers saw how inefficient it was and realized to cover a large majority of the country they would need more transponders. Since there is a limited number available in any particular spot, they arrived at spotbeams. The spotbeam basically is a signal that is narrowly aimed at a particular geographic area. So, in a "CONUS" (Continental US) beam, one antenna beams a huge radio signal that soaks the entire country. In a spotbeam, several antennas shoot a small beam over just the targeted area. The point of this is that with separate antennas and beams, they can send the locals for Dallas on the TP20 beam covering Texas and the Philly locals on TP20 on the beam covering Pennsylvania. This way, they don't have to waste bandwidth sending locals to areas that cannot view them. It works in the same way that there's a TV channel 6 in say Birmingham, AL but not in Atlanta, GA; but there is a TV channel 6 further up the East Coast. Because the signals are far enough apart to not interfere, they can send different content on the same channels.
Here's an even more in depth explanation with pictures:
http://www.sadoun.com/Sat/Products/Dishnetwork/Dishes/Spot_Beam_Short.pdf
