Can someone give a brief explanation for it? I heard about it once and I couldn't wrap my head around it, and the Wikipedia article wasn't much help either.
In most languages, there are (at least) two fundamental types of verbs. Transitive verbs require two nouns:
Alice hits Bob.
And intransitive verbs require one noun:
When the verb is transitive, there needs to be some way of marking which noun is doing the action, and which is having the action done to it. In English, this involves the placement of the nouns: the noun doing the action goes to the left of the verb, and the noun it's done to goes to the right. In Latin (and German and Japanese), this involves putting different markers on the two nouns.
The question is, then: what sort of marking do you put on the noun attached to an intransitive verb? Is it doing something, or having something done to it?
In English, we treat it as a doer. Which makes a certain amount of sense.
Alice eats the pie.
But sometimes that single noun isn't really doing anything, and it's still marked as a doer.
Bob broke the window.
The window broke.
English is called a nominative-accusative language, because it treats the noun on an intransitive verb as the doer. Languages which make the opposite decision are called ergative-absolutive.
Some languages, however, don't want to choose one or the other. They use one system in one circumstance, and the other system in the other circumstance. The noun attached to an intransitive verb is always marked with the "direct case". And with a transitive verb, one of the nouns is marked as either "thing doing the action" or "thing the action is done to", while the other is "direct".
So you could have:
Alice-DIRECT eats the pie-THING DONE TO.
Bob-DOER breaks the window-DIRECT.
The window-DIRECT breaks.
While complicated, this is in some ways the most logical system. Since "Alice" is marked the same in both sentences, and "the window" is marked the same in both sentences.