Are they big? Yes and no. It's the kind of show that you don't necessarily watch every night, sometimes you can go weeks or months without watching, but you always know it's there to provide great laughs when you do tune in. Also you will hear in the news or through gossip about some celebrity making a fool of themselves on the show or a controversial joke that was made. So they don't get huge ratings and not everyone watches all the time, but they fill the perfect time slot when people are just going to bed, so it gives you something light-hearted and comforting to fall asleep to. And that can have a big impact on people.
I remember the first time I saw Conan I was camping with my family. We were staying in a small trailer with a little 13 inch TV, and it felt so late to me (I was only about 10). My dad and I were the only ones up. I remember thinking how much I liked Conan as I fell asleep listening to his voice and the laughter of the audience. Good times!