A conversation is one customer's thread with your team about a single matter, however many messages go back and forth in it.
A customer emails to ask where their parcel is, you reply with tracking, they reply to say it arrived damaged, and you arrange a replacement. That is one conversation with several messages. Many helpdesks use the word ticket for the same thing.
Counting conversations rather than messages gives a fairer picture of workload. Ten back-and-forth messages about one return are still one piece of work.
Hobson brings email, live chat, Instagram, Messenger and contact forms into one inbox, and every conversation gets a drafted reply. Hobson plans are priced by conversations per month. Imported history and spam do not count, and at the plan limit drafting pauses rather than adding an overage bill. See pricing.