It was believed that people couldn't always control their lives, fate had a handle on them and no matter what they did, fate would win the fight. Examples of this would be Romeo and Juliet as they are 'fated' to fall in love - star crossed lovers. Or in King Lear when Kent bemoans his unavoidable 'fate.'
In The Winter's Tale the gods play a very active roll, as Hermione calls on Apollo to be her judge. It seems very natural in the play, but if anyone tried that in today's courts they wouldn't get anything except maybe called crazy. Hermione boldly cries, "Apollo be my judge" and is even seconded in this motion. Leontes also eventually admits that he has been rejecting the gods will. "Apollo's angry," he morns after his son has died suddenly.
Lastly, the play itself supports this belief in the gods. Hermione is innocent, and so when the Apollo (through the oracle) declare this, his existence as an all powerful being is supported. When Leontes son dies suddenly, just as prophesied by the oracle, this also supports the idea that the gods are an unstoppable force in the world of The Winter's Tale.
