The phrase "deep respect and trembling" uses two similar ideas to emphasize the importance of honoring their masters. (See: [[rc://en/ta/man/translate/figs-doublet]] and [[rc://en/ta/man/translate/figs-idiom]])
Here "trembling" is an exaggeration used to emphasize how important it is that slaves obey their masters. Alternate translation: "and fear" or "as though you were shaking with fear" (See: [[rc://en/ta/man/translate/figs-hyperbole]])
Here "heart" is a metonym for a person's mind or intentions. Alternate translation: "with honesty" or "with sincerity" (See: [[rc://en/ta/man/translate/figs-metonymy]])