Why do I need to know papoter?

It's a slang term and one that is used in casual conversation, especially if you're chewing the fat over drinks.

What does it mean?

It means to chatter, to chinwag, to chitchat, to prattle, to natter – a casual term for talking that also has the sense that the subject of the conversation is not particularly serious.

Au café je papote avec les meufs – At the café, I chat with the girls

If you're too busy to talk right now you could graciously excuse yourself by saying

J'aimerais rester et papoter mais j'ai rendez-vous chez le vétérinaire pour mon chat – I'd love to stay and chat, but I have an appointment with the vet for my cat.

If you have some particularly talkative colleagues you could tell them 

Si vous pouviez finir de papoter, on pourrait peut-être travailler un peu – If you can lot can finish up the chitchat then maybe we can do some work.

Or if you're a mean boss you could say Je ne te paye pas pour papoter – I don't pay you to natter.

Slightly more formal but with roughly the same meaning is bavarder. So if you call someone une fille bavarde – that means a girl who pretty much never stops talking.