Comedy Cellar questions to reserve and how it works.

Hi all, I am visiting from Europe and would like to go one night to the comedy cellar, I am already looking into make a reservation because I heard and read how difficult it is to have a spot on the day.

I am just having a hard timing understanding how it works and hopefully someone would be kind enough to ELI5.

Let’s take, as an example, the 15th of Jan, I see a lot of time slots separated by 15 minutes. What does this mean? And by experience what’s the best hours to go in?

Thank you all!!