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.