Contributed by: R. Ezra Mizrahi
Hoshanah Rabbah is the final day of Hol Hamoed Sukot, and is considered the final day of Yamim Noraim.
Over the holiday of Sukot, the Gemara tells us that the world is judged on the level of water supplies for the upcoming year. Hoshanah Rabbah is the culmination of this most-important judgment, a judgment of the most important aspect of sustaining human life - water. This is one reason for the name "Hoshanah Rabbah". "Rabbah " means great. The day is a "great" important day, as described above.
Another reason for the name is because we repeat the word "Hoshanah" many times during the morning prayers. Therefore, the day is called "Hoshanah Rabbah", "Rabbah" meaning "many", i.e. the day of the many Hoshanot
We turn now to Shemini Aseret, which begins this evening. Shemini Aseret is the extra day that closes the holiday of Sukot; Hence the name "Aseret"- to stop or to end (the holiday of Sukot).
As the midrash tells us the following parable: imagine a king invited a guest for seven days to his palace, and when it came time to leave, the king did not want the guest to leave and asked for him to remain one extra day. This is the extra day we stay with Hashem, our King, Shemini Aseret. (Outside of Israel, Shemini Aseret is separate from Simhat Torah making two real days, but in Israel they celebrate one combined extra day, Shemini Aseret that is also Simhat Torah.) Rabeynou Bahye writes on the level of holiness of Shemini Aseret. He compares the seven days of Sukot to the seven days of Pesah, and the eighth day of Shemini Aseret to the fiftieth day of the Omer, the holiday of Shavouot. This is why Shavouot is also called "Aseret" (as it stops the Omer). Here we learn that Shemini Aseret is equal to the day the Torah was given to us! May we merit a year of blessing in all we do, and added success in our studies.