Hi, Keven --
Proofs are collector coins that are struck on specially prepared coin blanks and made with polished dies, resulting in high-quality coinage. For the most part, proof coins aren't rare and they aren't necessarily always very valuable, but they are nevertheless special pieces that appeal to collectors who want specimen-quality coins for their collections.
Here's some more info about sets of proof coins:
http://www.coinvalues.com/library/us-mint-proof-sets-vs-uncirculated-sets
Best,
Josh