What does 'to share a connection' mean?

[Nobody]

Hi,

Tom and Mary shared a connection as they talked about.....

What does 'to share a connection' mean here?

Thanks

[Mister Micawber]

.
Without further context, it means that they enjoyed a common memory/experience.
.
_________________
Native English teacher at Mister Micawber's

[Jamie (K)]

It can also mean that they shared some emotional feeling of attachment to each other because of the subjects they were talking about.

[Nobody]

I see! Thanks!

[SkiIucK]

Or "We share the same Internet connection"...