Splendor and splendour mean exactly the same thing: great brightness, beauty, or magnificence. Splendor is the American spelling and splendour is the British one, so a British writer describing a cathedral or a sunset should reach for splendour.
The core difference
The words share one meaning; only the spelling changes between American English (splendor) and British English (splendour).
- splendor — American spelling: The splendor of the cathedral left tourists speechless.
- splendour — British spelling of the same word: The splendour of the Scottish Highlands is hard to describe.
How to tell them apart
Both words come from the Latin splendor, from splendēre, meaning to shine, so the roots and the meaning are identical. British English simply keeps the older -our ending that American spelling reform dropped in favour of -or.
The confusion tends to appear when a British writer's spellchecker is set to US English, or when copying text between American and British sources. Stay consistent with whichever variety of English the rest of the piece uses.