Even though Ruth was originally part of Hebrew scriptures, Christians today still embrace it as a holy and sacred text. They've got it tucked away in a little section known as the Old Testament. But that's just for safekeeping.
Why is the story of a Moabite woman who converts to Judaism part of the Christian canon? We're glad you asked (because we sure do like answering questions). See, Jesus and all his original followers were Jewish, they would have read Ruth's story as sacred scripture. When people started paying attention to Jesus, it was because they thought he was the Jewish messiah who would come from the line of David. Yeah, he was kind of a big deal.
As we know from our story, David's line runs straight through Ruth. In fact, Matthew's gospel even features her in the genealogy of Joseph—"Boaz the father of Obed by Ruth" (Matthew 1:5). That makes Ruth a really-really-great grandmother of Jesus. Not too shabby.
But because Christians like to put their own unique spin on things, Ruth has a slightly different place depending on whether you open a Christian or Jewish Bible. In the Old Testament, Ruth is wedged between Judges and 1 Samuel (if you blink, you'll miss it). This order is sort of chronological. The first line of Ruth tells us it takes place "in the days when the judges ruled" (1:1). The last lines end with a mention of David, who first makes his appearance in 1 Samuel. Perfect.
Different Christian denominations have different views about our leading lady. Missouri-Synod Lutherans commemorate Ruth in their calendar of saints on July 16. We think sainthood really becomes Ruth (source).
For the United Church of Christ, Ruth is part if the "lowly" lineage of Christ and a reminder that we're all connected in one way or another. Even people who are from another country. Especially if that country happens to be one we're constantly at war with. We don't think they're just talking about the ancient Israelites anymore (source)
The Roman Catholic Church mentions the Book of Ruth as a story that "bear[s] moving witness to an elevated sense of marriage and to the fidelity and tenderness of spouses" (source). Um, sure. That's one way of looking at it. Ruth is also named in a list of awesome biblical women, which naturally culminates with Mary because, for Catholics, she is the awesomest woman of all (source).
In the Hebrew Bible (which is what Christians would refer to as the Old Testament and what Jews would refer to as just the Bible), Ruth is part of the last third. Jewish scripture is divided into three sections—Torah, Nevi'im, and Ketuvim. Ruth is part of the Ketuvim (which means "writings" in Hebrew). It's kind of a catchall category for everything that doesn't fit with the first two—the books of law and the books about the prophets. Ruth is in pretty good company with loads of other famous biblical texts, likes Psalms, Proverbs, and Job, just to name a few.
Ruth is a pretty well respected lady in Judaism. Not only is she King David's great-grandmother (which makes her kind of a big deal), she's also celebrated as a Jewish convert. Here you have a girl who wasn't born into the Jewish faith, but who married into a Jewish family. Eventually, she embraced the religion of the ancient Israelites and their God, Yahweh. So, yeah, big gold star right there.
The story in the Book of Ruth also reflects the Jewish concept of chesed. That's just a fancy Hebrew word that means loyalty and faithfulness. In Jewish tradition, God is faithful to Israel and they (for the most part) are faithful right back to him. Our girl Ruth sticks by her mother-in-law even when she doesn't have to and gets rewarded in the end with a rich husband and lots of barley fields to tend to. That's just a little hint to the Jewish people from the author of Ruth: stick with Yahweh and things will be going your way (source, p. 240).
Today, the Book of Ruth is generally read as part of Shavuot services. The holiday celebrates the giving of the Torah. It's a late spring festival (falling sometime between May and June every year) and it centers on the end of the spring harvest season. That's one reason why Ruth's tale might be featured here—the whole barley harvest thing is a pretty big part of her story. No barley means no Boaz, and we couldn't have that, could we?