"I have one apple."
You can always try Wikipedia: http://en.wikipedia.org/wiki/Accusative The article might be understandable even for non-linguists. Briefly: Accusative is the case of direct object. When you use a verb that does something with some other thing, for example haben (to have), it takes this other thing (object) in accusative. In this sentence “I” is a subject (the doer of the action of having, WHO has?), whilst “an apple” is an object (the recipient of the action – WHAT is being had?). And an object of such verbs (they are called transitive) is in accusative.