In general, each Crate contains a specific set of items. When a Crate is unlocked, you'll receive a random item from the set the Crate is from. If a Crate has promoted (themed) items, those items always have higher drop rates. You can find actual drop rates by tapping the Info icon near a Crate.

There are a few different Crate types. Most Crates give bonus Materials. If you get a copy of an item you already own, you'll receive additional Materials instead.