Why do Ashkenazim read Megillat Rut on Shavuot? There are many different answers to this question, varying from the simple connection of Rut accepting the Torah to a Gematria to the lineage of King David. In fact, these different reasons may also be connected to each other.
Shavuot may be simply summarized as the day on which Hashem gave us the Torah. Rut originally did not need to follow the Mitzvot of the Torah, since she was not Jewish. In accordance with our tradition of dissuading converts, her mother-in-law, Naomi, repeatedly told Rut to go back to her nation and not to convert. Rut was young and beautiful and could find a husband among her people. When her sister decided to leave, she easily could have followed her and returned to Moav. But Rut insisted that she was going to stay with her mother-in-law. Rut ignored her own needs and did a great Chesed, taking care of Naomi instead of herself. She accepted the Torah by free choice and with love. Therefore, Rut exemplifies the meaning of Shavuot.
Teshuot Chein computes a Gematria (numerical equivalence) connecting Rut with Torah. The name Rut is 606: Reish (200) + Vav (6) + Tav (400). How does 606 reflect learning the Torah? Rut kept the 7 Mitzvot Bnei Noach even before converting. When that 7 is added to 606, it becomes 613 – the number of Mitzvot in the Torah!
The Bechor Shor points out that we read Megillat Rut on Shavuot to remember that David was born and died on Shavuot. Shemuel (prophetically) wrote Megillat Rut to commemorate the departure of King David from this world and to show the lineage of King David. Rut merited being an ancestor to King David because of her amazing acts of kindness to Naomi.
Rut led a difficult life. Yalkut Shimoni explains that we read Megillat Rut on Shavuot in order to teach us that man receives the Torah only through suffering and affliction.
As we listen to Rut being read on Shavuot, we should think of all the different reasons for the story and their connection to each other. If we read it in depth, we will gain extra insight into the true meaning of Chesed and the rewards one receives for following the Torah.
-Adapted from the Book of Our Heritage