In American and Scotch whiskies, an age statement is a declaration of the age of the youngest whisky in the bottle. Age statements in these two countries are strictly enforced, so you can rely on their accuracy. This is also true for other countries like England, Canada, and France.
Age statements for Spanish rums, and generally for those of other former Spanish colonies, are based on the oldest rum in the blend, or sometimes are just straight up bullshit. For more information about misleading rum age statements, check out this article.
You’ll also see “no age statement” abbreviated as NAS.
Whiskies with no age statements are growing increasingly popular, and you even see a few high end and expensive bottles with no age declarations. While I’ve tried some good younger whiskies and rums, I think that the process of omitting age statements is bad for consumers, as it makes it tougher to tell what you’re drinking.