In terms of definition, there isn't one, they both mean the same thing. However, with a 'u' is British English, without is American English. This is a common occurrence with other words (e.g. colour/color)

Spellings with a 'u' or an 's' are typically British English. Those without the 'u' or with a 'z' are American. eg. Favourite vs favorite Colour vs color Analyse vs analyze British English words also tend to use a French influence in the spelling of certain words. eg. Centre vs center Metre vs meter Theatre vs theater

Both are the exact same. However, "favourite" is British English and "favorite" is American English. There are many words like this, for example (American/British): color/colour flavor/flavour neighbor/neighbour Hope this helped!

Favorite - American English Favourite - British English So, the meaning is the same, and writing is a bit different.