An Explorer is a type of Starfleet ship.
This designation was only used from 2355 to 2371 and applied mostly to the Galaxy class starship. The Galaxy class was an attempt to have one class of starship to be able to do any job in Starfleet. Since Galaxy class starships had large modular sections, sometimes the ship could be well outfitted for deep space exploration.
This wasn't the only configuration the Galaxy-class could be arranged in, but it was the one that emphasized the "Exploring Strange New Worlds" image that Starfleet sought to present during that time period.
A more technically correct, but boring term for the Galaxy-class would be super-heavy-multi-role-cruiser.