Other experts will better explain, but Proof is just the way a coin is minted. It users higher quality dies, stronger strikes, etc. It could be silver, copper or aluminum foil - the metal isn't important - it's the METHOD that determines a proof. For example, there are Lincoln Cent Proofs and Jefferson Nickel Proofs and neither of those have any silver at all.
Proof coins as Pocket Change said are just a different type of coin. They are coins minted for collectors, and they are struck with stronger strikes, better dies, polished plancets, etc. Not all of them are silver. Only dimes minted in silver that are the pre-64, and then 1992-present, and they are for the silver proof sets. There are two types of proof sets that have different composition, the clad and the silver. And not only the dime is silver, the quarter and half dollar are also. So basicallly to answer your question "why are there a lot of dimes after 1965 silver?" because they are just another thing minted by the mint for collectors. But only post 65 dates that were minted with silver are 1992-present. Does this help at all? Phoenix
I am not positive but think that the proofing process turns the surface of a coin into a thin layered crystal, thus the excellent light reflection.
"A lot of dimes" and "all coins" are two different things. When you say "all proofs", I presume you mean "all proofs of 10c and higher denomination". There are proof pennies and nickels, but they never have silver. Many of the 10c and higher proofs have silver when their circulation counterparts are clad, but not all. And Sac $1s aren't silver, but there are proofs.
This is the only type of proof we have in Canada. Gold plated penny, loonie and toonie and silver plated on the 5 cent, 10 cent, 25 cent and 50 cent.