The story of Ruth takes place between the 12th and 11th centuries, B.C.E. Naomi and her husband, Elimelech, immigrate to Moab, a nation bordering the land of Judah, to escape starvation. Elimelech dies, and Naomi's sons both marry Moabite women.
Approximately ten years after the marriages, both of Naomi's sons die. Naomi is left with no blood relations, and she wishes to return to her former home in Bethlehem. Her two daughters-in-law, Orpah and Ruth, request to accompany her to Judah. Naomi tries to dissuade them, telling them how hard life is for the Jewish people.
While Orpah is convinced to stay in Moab and remarry, Ruth refuses. She wishes to remain with Naomi and become Jewish. She says, "[…] wherever you go, I will go; wherever you lodge, I will lodge; your people shall be my people, your God shall be my God" (1:16). With this statement, Ruth officially converts to Judaism.
Naomi and Ruth return to Bethlehem. Naomi was correct - life is hard for the two women. To avoid starvation, Ruth becomes a gleaner and collects extra grains on the farm of Boaz. Boaz is a distant relative of Elimelech, and could potentially be a new husband for Ruth.
Boaz, upon realizing that Ruth returned from Moab with Naomi, treats Ruth with special dignity. He asks her to work on his farm for the remainder of the season.
Naomi realizes that if Ruth married Boaz, her deceased son's name could be carried on. Naomi insists that Ruth dress in her finest clothes and go to Boaz's tent at night. She instructs her to kneel down in front of Boaz and ask him to take her as his bride.
Ruth goes to Boaz's tent in the middle of the night and lays herself at Boaz's feet. Boaz is, of course, extremely flattered by Ruth's actions. Boaz is significantly older than Ruth, who is only in her late twenties at the time.
The two marry and their first son is named Obed. Obed continues the lineage of Naomi's son. Obed eventually becomes the grandfather to King David and, as is written in the Torah, the Messiah must come from King David's lineage. Logically, the Messiah must also trace their heritage back to Ruth.
Even though she is a convert to Judaism, Ruth is one of the most respected women in the tradition. Rabbis use her story to show that true "Jewishness" is judged not by ancestry, but by acceptance of God and the mitzvot. Indeed, it is from this convert's line that the savior of the Jewish people must be born.
Sources: Telushkin, Rabbi Joseph. Biblical Literacy: The Most Important People, Events, and Ideas of the Hebrew Bible