What is the purpose and meaning of the Chair of Elijah? I understand that (some?) synagogues have a chair called the Chair of Elijah. Does this mean that it is a special chair that is set aside for Elijah? Will the Messiah sit there when he comes? Are other people allowed to sit in it? Is this practiced in every Jewish synagogue?
Having prayed in many different Synagogues that are from all the spectrum's of Orthodoxy, I have never come across a chair that is left vacant for Mashiach. Perhaps this is being confused with the Kisai Shel Eliyahu which many Synagogues have, and is used by a Bris. However as per Sefer HaZichronos many times others do sit on the Kisai Shel Eliyahu.
The chair of Elijah is not a seat for the Messiah, and in most synagogues it's a ceremonial chair kept in storage 90% of the time. And, as Gershon mentioned, people do sit in it, both ritually and otherwise.
Some synagogues don't have a special chair just for Elijah, but use the closest chair to the Bimah for circumcisions; so people sit in it all the time.
I was today in the synagogue in Cavaillon France one of the oldest in Europe. They and apparently also Carpentras have a chair on a podest high up in a corner of the synagogue which you can not even get to it. So it seems there was such a thing once.
I hesitate to give this answer, but there is a concept called "Moses' Seat" in the christian scriptures. (See Matthew 23:1-4.) The verse basically says that the scribes and pharisees sit in Moses' Seat. There were two theories about this verse: 1) That in ancient Israel, there was a physical/symbolic chair in synagogues where the wisest person (man) in the community sat; 2) it is purely a metaphor.
Having said that, I need to say that I do not view the christian scriptures as holy in any way. I am just offering up something that might add some clarity here.