A hat that is often erroneously referred to as a fedora, which has a wider brim.
The main way to distinguish a Trilby hat is by its shorter brims, in fact, so short that they don't give sun protection for the eyes and their purpose is just for fashion. Trilby hats tend to have its back trim turned up. In media, however, artists usually won't draw a trilby with it's trims turned up or down.
Do not confuse with bowler hat, which have a rounded crown.
Examples
Trilby with back brim turned up and front brim turned down
Trilby with flat brims
Non examples
Fedora, brims are long enough to give sun protection.
Porkpie hats are similar to trilby, but they have a short flat crown.
