“I’m just nipping out to get some milk!”
When we “nip” somewhere we go there quickly, so “to nip out” means simply to go out for a short time, in Italian it’s like “fare un salto.” We often say “just” to emphasise we will be quick.
“Could you just nip out to get some bread, please?”
“I’m nipping out to the supermarket to get a few things for dinner tonight.”
“Shall we nip out for a quick coffee?”