Why are temple ordinances performed?
This is a tricky question, because I can think of many different answer, on many different levels. For starters, an "ordinance" is a Mormon term which more or less corresponds to the term "sacrament" used by other churches. Temple ordinances include (a) some ordinances for the living, such as a marriage ceremony, and (b) some proxy ordinances performed by the living in behald of deceased individuals, such as a proxy baptism. I'll discuss the proxy ordinances, since I think they're the most confusing.
One answer is, temple ordinances are performed because that's what God commanded us to do. Mormons believe that Joseph Smith was a prophet of God, and that among other things, God commanded Smith to have the members of the church perform these temple ordinances.
Of course, the logical follow-up to that is "Why would God command that?"
So, a second answer is, temple ordinances are performed because they allow deceased people to accept the gospel.
For example, Christ taught that people must be baptized in order to be saved (John 3:5-- "Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God"). He also taught that people must keep the commandments (Matthew 19:17-- "if thou wilt enter into life, keep the commandments"). Similarly, the apostles taught that one must have faith in Christ to be saved (Acts 16:31-- "Believe on the Lord Jesus Christ, and thou shalt be saved", Galatians 2:16-- "...a man is not justified by the works of the law, but by the faith of Jesus Christ").
Yet countless people have died without having the chance to be baptized, without having learned of the commandments, without having learned of Christ. Mormon doctrine teaches that those people will be able to learn of the gospel in the hereafter. However, they must still for example accept baptism as a sign of their covenant with Christ. Since one cannot be baptized as a spirit, we people with bodies are baptized in behalf of the deceased. We do not generally know which deceased individuals in fact are desirous to be baptized by proxy, so for now Mormons take a "shotgun" approach-- we perform proxy baptisms for all people (starting with our own ancestors). That way, we figure, the deceased individuals can determine for themselves whether they accept the proxy ordinances or not.
Another logical follow-up might be, "Why on earth would God design things that way? It sounds so inefficient!"
I think that's an excellent question, and one not often considered by most Mormons. (Most Mormons would probably answer, "That's just the way it has to be.")
So, a third answer is, (in my opinion), proxy temple ordinances are mainly for *our* (the living) benefit. I think God is trying to teach us a lesson. I think the reason the temple ordinances were set up the way they were, is very much for the benefit of the proxy performers, and not just for the benefit of the proxy receivers. We are blessed in all kinds of ways as we perform this service for the deceased.
For example, part of temple work is "family history", i.e., learning about your ancestors. I think it is a great blessing for *anyone* to learn about their ancestors, and I am very grateful that the LDS church's emphasis on this has enabled me to learn about my heritage. I have been blessed by learning what sort of challenges my ancestors faced, and how they dealt with them. My life would be much poorer without this aspect.
Another thing I have in mind is that when temple service is being performed, it is really *service*, in that it is for other people, and it helps one develop selflessness, in the way that any service does. This is also a blessing. Going to the temple helps you forget about (as in "put in perspective") your own cares and concerns in much the same way that helping a friend with a move does.
These types of blessings are real, and they help develop us into better people.