It's different for each person (not always) but the day whenever you created your Stake account. You can view this by checking out your statistics page. It should be listed at the top.
I think to make the Stake Birthday more fun for the community the amount that is given to everyone on their actual Birthday and not just when they created their account, should be split 50/50. That way both of the birthdays feel fun and rewarding!
So if you receive $10 for your Birthday it would be more like:
Birthday: $5
Stake Birthday: $5