That's the particle which connects two sentences together. English equivalents for that would be: to; in order to; so as;
Uczę się języka polskiego, żeby czytać książki Sapkowskiego w oryginale.
I learn Polish in order to read Sapkowski's books in the original.
Poszedłem do cukierni, żeby kupić pączki.
I went to the baker to buy donuts.
Zarejstrowałem się na italki, żeby porozmawiać po angielsku.
I signed up on italki to speak English.
You can also use synonyms like: by; aby; interchangeably. Notice, that always before those words (by, aby, żeby) you have to put a comma.
I hope I've helped you out with that. By the way, be carefull with Polish spelling. You made the typo of the word "żeby" in the title. "Żaby" mean frogs :D