Both forms are correct.

Both spellings are correct and the pronunciation is also the same (two correct pronunciations for both words: fay-vuh-rit or fay-vrit). The only difference between favourite and favorite is that the former is used in British English while the latter in American English. There are much more words in British and American English sharing the same spelling problem -or vs -our. The history of deciding that -our ending stays in BE and simpler -or remains in AE goes back to the debate between two lexicographers – Samuel Johnson (British, who preferred -our form) and Noah Webster (American, who was an advocate for making English used in America really American). This decided on the simpler form or -or ending in American English words.

Correct spelling, this spelling is used in British English.

Correct spelling, this spelling is from American English.

Definition of favourite/favorite:
1. noun, someone or something special and preferred among others; used also for someone who we consider the best in competition
I love films with Leonardo DiCaprio. “Inception” is my favourite.
He was the favourite in this race and he won.
2. adjective, most liked, preferred
Joe’s favourite colour is blue.