The phrase often suggests a celebration or a very enjoyable outing. Graduation's tomorrow, let's paint the town red!
Pro Tip 2/3
Not Literally
The phrase is figurative, meaning to have a good time, not actual painting. They're not really painting anything, they're just going to paint the town red.
Pro Tip 3/3
Nightlife Fun
It's usually used when people go out at night to enjoy many activities, like dining and dancing. We've been working hard all week; it's time to paint the town red!