A transversal, according to one definition, is a "line that cuts across two or more (usually parallel) lines. There are two different ways that I've described transversals to students. After describing each, I will comment on a helpful way to use these descriptions in teaching later geometry topics.

Goalposts
Since transversals are described as cutting across "usually parallel" lines, I tell the students that the parallel lines are like the uprights of a football goal. A transversal is a line that connects the uprights. I've seen students light up with sudden understanding when it's put that way. Once they see where they goal uprights are, they can always find the transversals.

Continents
The prefix "trans" means across, and is used in the word "transcontinental," which means "across the continent." "So," I say, "you have an east coast and a west coast; these are your two lines. And a transversal is any line that represents a transcontinental voyage." This way of explaining a transversal has the added bonus of reminding us that two lines don't have to be parallel in order to have a transversal; the east and west coasts of the United States are not parallel, but there are many transversals cutting across them.

Transversals, Interior, Exterior
Somehow, the idea of "internal" (as in "alternate interior angles") and "exterior" (as in "alternate exterior angles") is a difficult idea for some students to grasp. However, both of the previous ways of describing transversals helps us to get a handle on these concepts...

Goalposts - If the ball goes through the goal, it is on the inside or interior. Students have no trouble visualizing that.

Continents - As with the goalposts, it's very easy to see that you are "in" the continent when you are between the two lines. Exterior angles are angles that are "in the ocean."