A transit telescope is a telescope mounted to allow rotation of its tilt between "more vertical" and "more horizontal", but cannot be otherwise aimed, i.e., no rotation through the horizontal. They are typically positioned so vertical rotation is north-south across the celestial sphere, i.e., along a meridian. One explanation of the name is that the target transits the aim of the telescope. The passage of a star across the field of view of a telescope is known as a transit.
Currently common are transit radio telescopes. Given their daytime usability, they have a chance to aim at a given target within 24 hours, and for all-sky surveys, they can cover the whole sky with just their single degree of freedom. And for the largest radio telescopes, available resources can be dedicated to a larger dish rather than the mechanism to horizontally rotate it. Some large past telescopes were built that way, and more recently, some telescopes dedicated to certain all-sky investigations are built this way.