1) A curse synonmous with any other monosyllabic swear word.
2) When used in conjunction with "...on your...," it becomes an expression synonymous with "Fuck you"; IE "Fuck you" means "Go get yourself raped," thus as the only thing fathomably worse than rape is teabagging, crying "Balls on your day, week, life... etc." is a curse on one's life.
3) Synonmous with "bullshit"; Thus, "Calling balls" is insisting that something is false or counterfeit, ala' calling bullshit or shenanigans.
1) (Upon stubbing one's toe): "Balls, that hurt!
2) That guy just cut me off in traffic! Balls on his day!