“The Reverend” is an honorific used in writing. It is used the same way as “The Honorable” is used with judges.
If one is being extremely formal or pretentious, it is acceptable to address a priest (or any clergyman who is not a prelate) as “Your Reverence”, just as one addresses a judge as “Your Honor”.
Addressing a priest verbally as “Reverend” is generally frowned upon, since we traditionally use the more affectionate “Father.” It is acceptable in some parts of the world, however, like in Northern Italy were priests are sometimes addressed as Reverendo.
So, more or less:
“The Reverend” (sometimes followed by Father) is used in addressing or introduction such as:
To:
The Rev. John Doe
123 Any Street
Beverly Hills, California 90210
United States of America
Or:
“May I introduce to you The Reverend Father John Doe of the Archdiocese of Rome.”