Unfiltered means the yeast (and other particulate) have not been filtered out. It is also common for unfiltered beers to have live yeast in the bottle, though pastuerizing is sometimes done (kills yeast, maybe to protect proprietary yeast).
If you have live yeast in the bottle, it sometimes will improve over time (for certain types). Once a beer is filtered or pastuerized, there is really no upside to aging it, it will start to degrade over time.
Yeast is also an excellent source of B vitamins. Folic acid is something that has a possible link to lowering risk of pancreatic cancer. On the downside, some peoples digestive systems have a hard time with yeast.
And to your comment on getting clear beer. Lots of ways of reducing yeast in bottle or keg:
-Racking to secondary - you will be amazed to see how much yeast is sitting on the bottom of the carboy just 1 hour after racking
-Cold crashing - bringing beer in fermenter down near freezing temps for 2-4 days. Usually seen as a time saving alternative to racking
-Extended cold crash or lagering - also usually done between 32 and 35F, an extended period of chilling can drop almost all yeast and protein, leaving really clear beer
-Finings such as rehydrated gelatin or Isinglass - latch onto particles and drop out of suspension
-Filter systems - not usally done in homebrewing, but its not too difficult to pass beer through a filter in between 2 kegs using CO2 pressure. Small size filters are needed however as yeast is pretty small.