How does Intercom define a web session?

That answers when the count is incremented, but not what triggers the "web sessions increased" goal...unless that goal just means they came to the platform once more than 24 hours after they were messaged?

The goal, in this case, is triggered when the "Web sessions" attribute for a contact, after they've received the message/Outbound communication, increases by 1. This increase happens in the event of either scenario outlined above.

Thanks for clearing that up. I'd suggest that the label "web sessions increased" is not the best way to label that then. To me it always suggested that there was some statistical rise in their activity, like they used to have one session every two weeks but since the message have gone up to three session a week, for example. I think a better label for this goal would be something like "returned to goal target after message"