1) Temples are considered Houses of the Lord, places we can go to commune with God, and no unclean thing can enter into the presence of God. So we preserve the sanctity of the house of God by certifying (through local bishops) that people entering in are obeying God's commandments and living in such a way that they will not offend the Holy Spirit in the temple. 
 
2) In the temple we perform religious ceremonies, epic rituals that are deep in their symbolism, substance, and language. The longest of these 'temple ordinances' takes over 2 hours to complete. Everyone is a participant in the temple cermonies. There are no 'observers'.  
 
The purpose of these rituals is to make promises to God to obey the Gospel. So only those who have been prepared and is currently living these commandments should go to the temple to make these promises.  
 
3) Most people who ask this question are actually asking, "Why can't I go see my son/daughter/grandchild/friend get married in the mormon temple?" 
 
The answer to that is because a Mormon marriage is not only a promise to each other, but a ceremony where the couple makes promises to God as well (as described above). If the parties are faithful to each other, they are sealed together for all eternity, not until death.  
 
4) Everyone is welcome in regular Mormon chapels and meetinghouses where we have worship services each Sunday. If you want to learn more about the temple, I would show up there.

"These buildings, different from the thousands of regular Church houses of worship scattered over the earth, are unique in purpose and function from all other religious edifices. It is not the size of these buildings or their architectural beauty that makes them so. It is the work that goes on within their walls. 
 
The designation of certain buildings for special ordinances, as distinguished from regular places of worship, is not new. This was the practice in ancient Israel, where the people worshiped regularly in the synagogues. Their more sacred place was, first, the tabernacle in the wilderness with its Holy of Holies, and then a succession of temples, where special ordinances were performed and where only those who met the required qualifications could participate in these ordinances. 
 
So it is today. Prior to the dedication of a temple, The Church of Jesus Christ of Latter-day Saints invites the public to go through the building and inspect its various facilities. But when it is dedicated it becomes the house of the Lord, vested with a character so sacred that only members of the Church in good standing are permitted to enter. It is not a matter of secrecy. It is a matter of sanctity." 
 
http://www.lds.org/temples/purpose/why/0,11581,1953-1,00.html

Mormons believe that all were members of the Heavenly family before the creation of the universe. Children of Heavenly parents and enjoyed the presence of Heavenly Father and Jesus. When coming to earth they pass through a veil of amnesia for the purpose of building faith. The temples are embodiments of sacred space during their dedications. After 1 year of covenant living as a new LDS Christian all are invited to enter the temple.