... one more aspect of connections. The Darcys are untitled, and presumably it's because they don't want to be, with the kind of family pride that scorns titles.

Connections mattered, because they increased influence -- your connections would be able to help you in some way.

Mr Darcy would have been looking for a wife with additional connections to the ones he already had -- one mark against a marriage to his cousin, who wouldn't have brought him any new ones.