Ball parties were really the only times when the girls had the chance to speak freely with the men they were interested on. Like, for example, Jane and Bingley's communication was only possible during those ball parties, and even Charlotte made a point of saying that Jane had to step up her game because ball parties seemed to be the only time she chatted with him.
As far as Elizabeth, she was able to also speak openly to Darcy during the second ball where they met. She made all her observations on him and she was actually able to score him off in a mini showdown that they had where she basically called him a snob for not dancing.
In general, balls were the parties that were understood as the "husband picking faires" and men were likely to make a strong acquaintance during a ball when the ladies show themselves at their brightest and prettiest, and where they also have the opportunity of demonstrating their talents in dancing and singing.
An example of an important moment that took place at a ball party was when Mr. Darcy and Elizabeth danced and when Jane and Mr. Bingley danced.
Ball parties were a type of social gathering that brought people together. Men who had interest in a particular woman would ask them to dance.