This one's weird, isn't it. I mean, who goes out with a tin of red emulsion paint and paints everything in town red? Strange.
But it can be explained in idiomatic terms ... thankfully.
Meaning[]
It means to celebrate by going into town and having a nice PARTY!!! Woohoo!
(Of course I once celebrated something by getting some tortilla chips and trying to mix salsa, sour cream and grated cheese to make the perfect tortilla dip. I nearly regretted that one.)
Use in Normal Speech[]
When warning of a celebration.
"I've passed my driving test, so if I'm late, it's because I'm painting the town red."
When explaining why someone's late.
"Anya passed her driving test today - she's painting the town red. That's why you've missed her, sorry."