It's hard to find a good pic, but I think this one will work.
View attachment 428671
The one on the left is a complete balancer, the one on the right is the two pieces separated (center hub & balancing ring/pulley). If you look at the hub potion on the right, you can see it has a rubber ring on it which separates the two pieces. This rubber ring allows for some back-and-forth give, thus dampening the pulses/harmonics coming through the crankshaft. Basically, the rubber acts like a shock absorber smoothing out the regular pulses of the crankshaft. With time and many heat cycles, the rubber becomes brittle and doesn't do its job as well. In a worse case situation the two will separate while running, then you have a weighted metal ring spinning 700-5000 rpm on the loose, but that's worse case and not common. Of course, the last time this came up Blaine mentioned he had recently seen a few failures. Yours may be fine, and a cheap parts store part may be worse. Just something to consider while doing this job.
Some engines use a balancer separate from a damper. A harmonic balancer combines the two, but that's irrelevant here and just FYI.