In horse terms, a roman nose is a head with a convex profile. It's most commonly seen in draft horses and is often considered a fault, or at least "common" in light horses (and a definite fault in Arabians and many pony breeds).
An extreme Roman nose - this would be considered a fault in any animal (Image source Amazona01 via Wikimedia Commons).
A more moderate Roman nose is perfectly acceptable on this Shire horse. (Image source Una Smith via Wikimedia Commons).