Please say this passage in simple words ( what does it imply?)

"The story elicits groans of recognition and prompts listening ESL practitioners to roll their eyes heavenward."

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When the ESL teachers hear the story, they recognize it from their own lives and experiences. It is an unpleasant story, so the teachers groan (=make a noise to express dislike). In the story, somebody behaves in a stupid or annoying way, so the teachers roll their eyes (=look upward to express exasperation).

This is probably a story about, for example, a student who refuses to do homework. All the teachers recognize and dislike this kind of student, so they groan, roll their eyes, and nod.

to elicit sth from sb = to prompt sb to do sth = to cause sb to do sth