Concetta is Prince Fabrizio's eldest daughter. She is also the only one of Fabrizio's children who gets much airtime in this book. She is generally a shy, proud girl. She is totally in love with her cousin Tancredi, and she gets her heart broken when Tancredi falls in love with Angelica and gets engaged to her.
On some level, Prince Fabrizio knows this is for the best. Tancredi is a social climber, and Fabrizio doubts that Concetta would make a very good wife for someone trying to rise in the world:
And would Concetta, with all those passive virtues of hers, be capable of helping an ambitious and brilliant husband to climb the slippery slopes of the new society? Timid, reserved, bashful as she was? Wouldn't she always remain just the pretty schoolgirl she was now, a leaden weight on her husband's feet? (2.47)
The answer to that last rhetorical question, of course, is yes.