Types
Proof sets are collections of high-quality coins assembled specifically to sell to collectors. Mint sets are "one-each" collections of coins, straight from a particular minting facility, that are also designed to be sold to collectors. "One-each" sets are collections of one of each denomination of coin.
Features
Coins included in a proof set have been created to a higher standard than those meant for circulation. They are usually very highly polished and stamped in such a way that the raised portions create a "cameo" effect. Mint set coins are simply those coins that could be circulated, but are diverted for collectors.
Potential
Valuation of mint sets and proof sets is dependent upon a number of factors, including condition of the coins and rarity of the issue.
Fun Fact
The U.S. Mint has produced specialty proof and mint sets over the years, including the "state quarters" and dollar sets honoring American presidents.
Time Frame
Proof sets have been in existence, on and off, since the 1800s. Production picked up in the mid-20th Century, when coin collecting became more popular.