Proof coins are struck from highly polished planchets and dies and then they will receive multiple strikes from the coining press at increased pressure. After the strikes, they are carefully placed in sealed holders. US Proof sets have long history back to 1795 in small scale to certain people but it became available to the general public in 1936. The production of proof sets was interruptted between 1943 and 1949, and between 1965 and 1967. Current year sets are available directly from the US Mint. You might also be able to get the previous years from there too as long as the supply lasts. You can get recent proof sets for less than $25. The old release like 1956 vesion can sell up to $60.

Here are some US Proof sets for sale on eBay.