It’s called kinetic typography, or kinetic typography animation. Here’s a nice example from the Vincentians (SSVP) of Australia.
The folks at wizMotions say
Kinetic typography is the art of animating text to increase its impact on readers by increasing the emotive and interactive quality of the text. Text is presented over time, becoming temporal rather than static. Even if you’re not familiar with the term, chances are that you’ve seen it in action.
Like other human relationships, successful communication between writer and reader depends on timing and mutual understanding. The ability to communicate emotion greatly contributes to achieving that understanding.
Here’s the best collection of kinetic typography possibilities I’ve seen in a while. It’s a powerful, artful mode of communication. Aaron Kitney of Creative Bloq put it together. Please enjoy 37 must-see examples of kinetic typography.