In a position facing another. Literally 'face to face'. Often now used in the sense of 'in relation to'.
The term is French and began to be used in English in the mid 18th century. The French spelling is vis-à-vis, that is, with the grave accent, although that is often omitted when written in English. It is now frequently printed, no doubt to French shrugs and mutterings, as 'vis-a-vis' or even 'viz-a-viz'.
When 'vis-à-vis' was introduced into England it was provided with two distinct meanings, both of which were in use from the 1750s onward. Oddly, it seems that these were both introduced by the author and politician Horace Walpole.
The first meaning was the literal translation from the French, that is, 'face-to-face'. Walpole was an incurable letter writer and, fortunately for us, many of his letters have been published in a collection of books, which provides the first citation we have of the term in English, in Letter to George Montague, July 1753:
"He was walking slowly in the beau milieu of Brentford town, without any company, but with a brown lap-dog with long ears, two pointers, two pages, three footmen, and a vis-a-vis following him."
What he meant by a 'vis-a-vis' in that letter was 'a small two-seater carriage, in which the passengers sat face-to-face'. These carriages were similar to the four-seater version that Queen Elizabeth uses each year to tour the course at the Royal Ascot race meeting.
The meaning was extended to apply to any person or thing that was facing another, for example, one's dance partner, someone sitting across the table at mealtime, couples meeting in the street, etc. Mary Berry included a citation of the first of these in Social life in England and France from 1780 to 1830, 1831:
It seems perfectly indifferent to them [the peasant men and women dancing] who is their vis-à-vis.
Secondly, it meant 'with regard to'/'in relation to'. Horace Walpole again, in Letter to R. Bentley, November 1755:
"What a figure would they make vis-à-vis his manly vivacity and dashing eloquence."
It is this second meaning that we have held on to. We can now safety substitute 'with regard to' for 'vis-a-vis' with little fear of misinterpretation.
If you frequent square dances, you are likely to find yourself 'vis-à-vis' with your partner. When the dance caller shouts out do-se-do (also spelled 'dosey doe', 'dozy-doe' 'do si do', 'dosado' etc.) you had better turn around, for what he really means is 'dos-à-dos' - in the original French 'back-to-back'. Dos-à-dos was employed as widely as 'vis-à-vis' in the 19th century, being used as a name for carriages, duelling partners - anything in fact where the participants are back to back.
See also - other French phrases in English.