Is this correct grammar?

You know how you say 'an apple' instead of 'a apple' and 'an octopuss', not 'a octopuss'? Well my dad tought me that you should put 'an' infront of words beginning with 'h', and I did that in an history essay, and the teacher marked me down for inncorrect grammar! Who else puts 'an' infront of 'h's?

The correct grammer( assuming you are in England) is than A goes before a constanant and AN goes before an vowel Anything else just isn't cricket!

It is used before an initial vowel sound and sometimes before an initial unstressed syllable beginning with a silent or weakly pronounced 'h'.

Examples include:
an honour
an hour
an historian (However, 'an history essay' is incorrect grammar; it's 'a history essay').

The thing that annoys me about grammar nazis, is that they falsely believe they own the language. Our language is whatever we use to communicate. We own it collectively and are free to modify it at will.

It's ordinary in spoken conversation to say 'an hour', and since written language is modeled after spoken language 'an hour' would feel natural to any reader.

In regard to 'history' personally, 'a' sounds more natural to me, 'I have a history essay due on Tuesday', but I probably wouldn't shoot someone for using 'an'.

For the purpose of an English class, I would simply parrot back whatever the teacher told you so you get good grades, but then use common sense in real life.

The real answer is that the English language is constantly changing, and your dad is applying correct but out-of-date rules. No one has changed the rules yet, so he is right, but almost no one sticks to them any more, so your history teacher (whilst a bit thoughtess not to explain) is probably just encouraging you to use modern English instead of something old fashioned. The rules are changing as we watch...

The historical reason for the 'an' in front of many 'h' words is that 'h's are all silent in French, so once upon a time the words we borrowed from French like 'hotel' or 'history' were pronounced without the 'h' sound. Odal's summary of how the rules currently work is pretty good, but also going out of date. The rules will probably catch up with modern usage in your life-time!