"To say uncle" is mostly used by children.  As with "pedir penico", it means to admit defeat or submission.  Usually pain is involved.  When adults use it, they are using it in jest and can be talking about sports, business, etc.

Johnny:  "Say uncle or I will hurt you some more!"

Billy"  "Uncle!  I give up!  Get off me!  You are hurting me!"

We plan to keep lowering our prices until the competition says uncle and we are the only business offering this service/product.