Proof
Silver proof coins are minted specifically for coin collectors. They are minted in such a way as to give them a highly reflective surface. Proof coins come in protective casings and are bought directly from the mint. They also come with certificates of authenticity that explain their composition (if you don't know if the coin is silver). Proof coins are never circulated.
Uncirculated
Uncirculated coins are freshly minted regular coins that were never circulated. Instead they were sold by the mint for collectors. Uncirculated silver coins have absolutely no visible wear. The highest quality uncirculated silver coins have no wear, even under a microscope.
Mint State
The mint state grade is reserved for circulated silver coins that look as though they are uncirculated. This is the highest grade a circulated coin can receive. In some circles, uncirculated and mint state are used interchangeably, but technically, they are different grades. No silver coins have been minted for circulation in the U.S. since 1964 however. Any coin with a later date is a clad coin, made with other, cheaper metals.
Fine Grades
Extremely fine silver coins have very light wear. An extremely fine coin's highest points (the points that get the most wear) are still well defined. At first glance, an extremely fine coin may look like a mint state coin. The very fine grade is the next step down from the extremely fine grade. A very fine coin has moderate but even wear on the high points of the coin. A fine coin has wear on the surface of the coin. All lettering should be still be readable on a fine coin.
Good Grades
A very good silver coin is well worn, with most fine details being nearly smooth. The lettering can be slightly worn off. A good silver coin is heavily worn, with a majority of the coin surface being worn smooth. Major images have little center detail but are still visibly outlined. About good coins are even more worn than good coins. The date must be readable, but it can be well worn.
Lower Grades
A poor (sometimes called fair) silver coin is a coin that can be identified as to type but not as to year. These coins are extremely well worn and can have holes or be bent. A basil state coin is a coin that cannot be placed as to type. This type of silver coin is basically a small metal disc worth nothing more than the value of its silver.