What does the end of analog TV mean?

A report from The Consumerist

Free over-the-air broadcasting will switch to a digital format on Feb 17, 2009. If you have an older (read: analog) television, and use an antenna, you may need to purchase a converter box in order to continue watching your favorite TV shows. Coupons for converter boxes are available from the FCC's digital conversion website.

Consumer Reports says that this infornation is proving incredibly difficult to convey:

Even among those who are aware of the switch to digital broadcasts, there is rampant confusion about what it will require of consumers. Among those consumers who are aware of the transition, over half (58%) believe all TVs will need a digital converter box to function, 48 percent believe that only digital televisions will work after 2009 and nearly one quarter (24%) believe they will need to throw away all of their analog television sets; none of which is true.