To understand why usted is abbreviated as Vd.we need a quick lesson in the etymology of the word, and the story of that pronoun also answers another question about Spanish, namely why the second-person pronoun usted (those used when talking to somebody to refer to that person) uses third-person verbs (those used to refer to someone other than the speaker and listener).
Why Usted Is Abbreviated
Usted had its origins during the colonial era, wher it was common to address nobility and other people held in esteem (or people who thought they were held in esteem) as vuestra merced, meaning "your mercy." Vuestra merced was used in much the same way as "your honor" is used in English today, with third-person verbs, i.e., we say "your honor is" rather than "your honor are." It began as an extremely formal type of address, eventually becoming the standard way of addressing people in higher positions as well as persons who aren't friends or family.
As is often the case with much-used terms, vuestra merced became shortened over the centuries. It changed to vuesarced to vusarced and eventually to vusted, which you may still hear, especially among older speakers, in some regions. Vd. was adopted as an abbreviation for that word or earlier forms and remains in use today, although Ud. is more common.
Spanish speakers tend to soften their consonants, so vusted eventually gave way to today's usted (which in some areas has its last letter softened so it sounds like usté). Like the earlier vuestra merced, it still uses third-person verbs (i.e., usted es for the formal "you are" but tú eres for the familiar/informal "you are").
As all living languages do, Spanish continues to change, and these days usted itself is being heard less often. In a change that has its parallels in English, much Spanish usage is becoming more informal or egalitarian. wheras at one time, strangers were frequently addressed as usted, it is common in some areas, especially among younger people, for peers to immediately address each other as tú. On the other hand, there are areas in which usted is used even among family members, and others wher vos is preferred over tú for family or close friends.
