This is the adverb of reverential. If you do something reverentially, you do it in a way that shows deep respect and admiration — you speak reverentially, you bow reverentially, you handle an old object reverentially. It is a formal, rather literary word. In everyday talk, people are more likely to say respectfully or with great respect. You will mostly meet it in writing, and often about voice, silence, or the way someone touches something they treat as special.