There are many important themes in the book of Ruth. The two main themes are: God's providence, and the idea of a kinsman redeemer.
The book starts off in the time of the Judges. It is a wretched time where people are doing what is right in their own eyes. All you need to do is read Judges to know how terrible the times are. In this context, it seems like God has abandoned his people. But God is silently working in amazing ways. After Naomi loses her husband and two sons, one of her daughters-in-law, Ruth decided to go with her. One of the most famous passages is:
"But Ruth replied, "Don’t urge me to leave you or to turn back from you. Where you go I will go, and where you stay I will stay. Your people will be my people and your God my God. Where you die I will die, and there I will be buried. May the Lord deal with me, be it ever so severely, if even death separates you and me.'"
When Naomi and Ruth come to Bethlehem, by chance, Ruth collects grain in the field of Boaz, who happens to be a kinsman, who also happens to take notice of Ruth, and who also happens to marry her in time. All of this seems like chance, but it is under the providence of God. This is important, because Ruth bears a son Obed. Obed bears Jessie, and Jessie will be the father of David, Israel's great king. To go back to the original context, the way out of the time of the Judges is through a great king.
Finally, Boaz through Jewish law is able to redeem Ruth and so he does. In Jewish tradition this is called a kinsman redeemer, and this was done, so that the deceased would not lose all of their land. This union, then, leads to a new epoch in Israel's history, the kings.