It is possible to replace the line "I listened with heart fit to break." with "I listened with my heart beating hard."
This line was taken from the poem "Porphyria's Lover" and the hyperbole is used to show the speaker's nervousness and excitement, by intensifying the speaker's heartbeat.
In this case, the figure of speech shows that the speaker's heartbeat is very fast and strong, to the point that he thinks his heart will break.
More information about hyperbole in the link:
https://brainly.com/question/2142709