Flavor and flavour mean exactly the same thing: the distinct taste of a food or drink, or the distinctive character of something. Flavor is the American spelling, flavour the British one — the same u-dropping pattern you see in color/colour and humor/humour.
The core difference
Flavor is the American spelling and flavour the British spelling of the same word for taste and character.
- flavor — US spelling, the taste of food or drink: The soup had a rich, smoky flavor.
- flavour — UK spelling, the taste of food or drink: The sauce has a lovely tangy flavour.
- flavour (verb) — to add taste or seasoning: The chef flavoured the rice with saffron.
How to tell them apart
Flavor/flavour traces back through Old French flaour ('smell, odour') to Latin flare ('to blow'). It originally referred mainly to smell before shifting over time to mean taste, which is why the word still covers a food's overall character rather than a single note on the tongue.
As with colour, humour, and honour, the spelling split is purely regional: American English drops the 'u', British and Commonwealth English keeps it. The word also stretches beyond food — 'the film captures the flavor of small-town life in the 1950s' uses it for a distinctive character or quality, not taste at all. Whichever spelling you pick, keep it consistent across a piece of writing.