So you have a kitchen with several ovens. You make roasts in those ovens, but your roasting pans are huge, and you could really get away with smaller ones. You decide you'd like to be able to fit two or three roasts in each oven instead of one, by using smaller roasting pans. Not too difficult is it?
Just like the old roasting pans, analog TV signals take up a lot of 'space' in the radio spectrum used for broadcast television. Digital TV signals take up less, because of the ability to compress the data somewhat and other efficiencies. Unfortunately, unlike roasting pans, switching signal types means breaking all the TVs in America. Not as easy of a choice.
The FCC and government decided that to make room available for more high definition broadcast programming, the switch to Digital TV ought to be made. Industry groups didn't want to change, people don't like change, but its a good change to make eventually, so they went ahead and set a deadline -- February 17th, 2009 in the United States of America. As of today, most people don't seem to yet be ready for the transition or don't understand what it is or what they need to do so Congress has agreed to delay it until June 12th of this year. In Canada, this isn't relevant until August of 2011.
There will be more annoying commercials until then, referencing the government's website about the transition. There will be retailers griping and consumers worrying, but its all very simple really: it probably doesn't matter to you.
Do you have satellite TV, or cable? Then it doesn't matter, breathe a sigh of relief and ignore all the commercials and warnings.
If you don't have either satellite or cable, you're watching TV through an antenna (either built-in or not). In that case, if you have it nearby or can find a copy elsewhere, check your TV's manual to see if it has an "ATSC" tuner. If it only has an "NTSC" one, you don't have digital TV support on it, and will need a digital tv 'box' unless you want to buy a new TV. No ATSC tuner, no free TV after June 12th.
If you can't find the manual for your TV, and you don't have satellite or cable, and you're worried you won't be able to watch TV, then call the manufacturer of your TV and ask them. The technicians at Sony or Panasonic or whomever should be able to assist you.
Now there are a whole bunch of other issues involved in the switch to digital, but very few of them will be beneficial to you, the consumer. Mostly, this is to make the FCC's and other regulators' lives easier and they threw a bone or two to the broadcasters as well to grease things along.