As we are in the last stretch before Rosh Hashanah, this Saturday night we will begin the special series of prayers called Selichot. Selichot are special prayers compiled together expressing regret on our past mistakes, lamenting on the Exile, and praying for the redemption. According to Ashkenazic custom, we begin these prayers on the Saturday night before Rosh Hashanah, with a minimum of four days of Selichot prayers before Rosh Hashanah. (When Rosh Hashanah is Sunday night like this year, we begin the week before to have the four day minimum.)
Why is there a four day minimum? In Temple times, before one would bring a sacrifice to the Temple, they would need to first observe it for four days to ensure that the animal is perfect for a sacrifice. Likewise, we have four days to look through ourselves to ensure that we are ready for Rosh Hashanah, the day of judgement.
Although the Selichot is specifically said after midnight on Saturday night and has nothing to do with Shabbat, nevertheless this Shabbat is called Shabbat Selichot.
If a Dentist needs some dental work, they need to go to another dentist, they cannot treat themselves. If someone is captured, they need an outside person to set them free. Likewise, for us to correct our ways and fix our mistakes we need some outside help. That is why we always begin the Selichot prayers Saturday night, and the Shabbat is called Shabbat Selichot. It is with the special serenity and power of Shabbat that we can approach the Selichot prayer series and correct ourselves as the final preparation to Rosh Hashanah.