It refers to the mission of the original starship Enterprise.

The Starship Enterprise sat there in front of them, looking like she meant serious business.

"We are the officers from the starship Enterprise. "

Like the starship Enterprise, museum curators are supposed to go where no curator has gone before.

I assume you were told you're aboard the starship Enterprise.

How many times had the crew of the Starship Enterprise been on hand to save the day?

This is not the kind of space that the Starship Enterprise set out to explore, however.

Jefferies designed the starship Enterprise and most of its interiors.

You're among friends, in the sickbay of the starship Enterprise.