To understand the answer to this question, we need to take a look at some Mormon beliefs.
To be specific, money, houses, cars, and other possessions are gifts from God. We have them because God blessed us with the qualities, hard work, family history, or whatever it took to acquire them. Mormons believe that we should be willing to give God anything he asks for because ultimately it's his stuff, not ours. We're just his stewards. God lets us enjoy our possessions and gives us the freedom and responsibility to use them as we will, but he also commands that we use them well. We need to be good stewards for him.
When it comes to money, Mormons believe that God has commanded us to support our church, the Church of Jesus Christ of Latter-day Saints. Here is why:
The Church of Jesus Christ of Latter-day Saints (the Mormon Church) claims to be the only church on earth that has the correct and complete teachings of God. Jesus Christ himself governs its affairs because it's his church. Therefore, Mormons believe that they have the most wonderful of all the gifts of God - the truth. And what do Mormons want to do with it? We want to share it! The fullness of the Gospel is such a beautiful thing, and we want our brethren to be as happy as we are. So we share it, or try to anyway. God has also commanded us to share it. It's his truth, and it's his work to teach everyone how to be happy and successful by knowing and living the Gospel.
So we've established that sharing the Gospel is an important goal for the Church. But sharing the Gospel takes money. The Church produces millions of copies of the Book of Mormon, the Bible, church videos, pamphlets, pass-along cards, and other items given to investigators for free. The Church also helps pay for members to serve missions, subsidizes educational institutions, provides natural disaster relief, runs various humanitarian efforts such as the Wheelchair Program, provides reasonable support and transportation for some church leaders, and publicizes videos and other advertisements about Jesus Christ and his Gospel. The Church also builds many temples, meetinghouses, and other buildings throughout the world and has budgets for church activities on all levels of the various branches of the Church. There is so much that the Church has to pay for!
Mormons believe that we need to help build up the Church, take care of the poor, and share the Gospel by obeying the Law of Tithing. The Law of Tithing says that we are to give God "one tenth of [our] interest annually," which is understood to mean 10% of our income. Church members are also supposed to give a generous fast offering, if they are able, when they observe the Law of the Fast once a month (going without food for two meals and then giving the money that would have paid for the two meals to the Church). The tithing is then used for the aforementioned purposes while the fast offering is used to help the poor. Church members may also donate money to specific causes (like building temples) if they wish.
So God only asks for 10% back and has promised that he will bless us if we do it. He has said in ancient times, "Will a man rob God? Yet you have robbed me. But you say, 'Wherein have we robbed you?' In tithes and offerings...Bring all the tithes into the storehouse that there may be meat in my house and prove me now herewith, says the Lord of Hosts, if I will not open you the windows of heaven and pour you out a blessing that there shall not be enough room to receive it." (found in Malachi) This commandment and promise in the Bible is a good one for Mormons to look to when it gets hard to pay tithing. Sometimes we need to be reminded that it really isn't our money; it's God's. We might have earned it, but God gave us the ability to earn it. God says that if we pay our tithing, he will bless us.
Yes, God requires us to pay our tithing, but we may choose not to. We can still participate in church activities if we don't pay tithing, and most people won't know it, but we don't get to go to the temple, and we won't enjoy the blessings that come in consequence of paying our tithing. We also will be keeping money that is not our own, but is God's. Many Mormons (including me!) have a testimony of paying tithing and can tell you that it has been a strength rather than a burden. To hear their stories and learn more about tithing and what it's used for, click on this link to visit Mormon.org. http://mormon.org/faq/topic/tithing