As @ Exuberant Islander says, it's just a funny language quirk - there are a handful of words and their derivatives that begin with a silent 'h', and you just have to learn them. The essential ones are: hour, hourly, honour, honest, honesty, honourable (with or without the 'u') heir, heirloom and the letter 'h' itself ( pronounced 'aitch') The optional ones are: the American pronunciation of 'herb' the now very outdated 'historic(al)' and 'hotel'. I'm not sure if I'd agree with Michael about words of French origin, though. Yes, the above words were originally French, but so were lots of other English words which we now pronounce with an aspirated h, for example: habit, haricot, hesitate, hospital, hero, humour, and many more. I can't think of a sensible reason why we say 'humour' with an 'h' but 'honour' without one. It's just one of those things... However, if you are deliberately using an actual French word in English, you can show your sophistication by missing off the initial 'h'. For example, 'hors d'œuvre' has no 'h' sound at the beginning, we say the French word 'hommage' ( a fancy alternative to 'tribute') à la française with a silent 'h', the expression 'haute cuisine' as 'oat cuisine' and we usually pronounce the surname of the politician François Hollande as 'olahnd'. I think that just about covers it.

In addition to the word families with "honest", "hour" and "hono(u)r" as roots, there is also "heir" (but not "heritage", "inherited", etc.) and, optionally in the US, "herb" (grass, not short for "Herbert"). Off the top of my head, I can't recall anything else. Also, some people (but not all) treat the words "historic" and "historical" (but not "history") as if the "h" is silent (i.e. say "an historic opportunity" instead of "a historic opportunity"), but also sometimes pronounce the "h" anyway, which I think is a funny language quirk.

Words with a silent "h" have French origins. If you speak French, this may help you. If not, then you will have to learn each word individually.

There are no "grammar rules" in vocabulary. Grammar rules work for grammar only.