As I understand it a counter swing is a fast swing you can perform immediately after getting hit by your opponent. It doesn't matter what direction you counter from or if you PB or not, just attack right after getting hit. The time window to execute it is small so you have to be fast. The big upside to countering is that you can use it to defend yourself and get a free hit in at the end. One downside to it is that if you do it often and predictably your opponent might realize it and slap you every time.
Source:
The Cult Dueling Guide 1.9 and
Noel's Dueling Guide [Up to date]
(Disclaimer: I don't really duel a lot so best some duel sneed tells you the ins and outs better)