Consider the following two sentences.

The king built the temple.

The king sleeps.

In many languages, such as English, the king is treated equally in both sentences, namely as the subject. But in an ‘ergative’ language there is no concept of a ‘subject’. Rather than drawing a distinction between subject and direct object—between nominative and accusative, as in the Indo-European languages, for example—an ergative language draws a distinction between ‘agent’ and ‘patient’, which is not the same thing at all. Such languages do not have nominative and accusative cases. In the first sentence the king is the agent of the transitive verb built, and is in the ergative case. In the second sentence the verb sleeps is intransitive, so there is no agent; the king is a ‘patient’ of this verb, just as the temple is a patient of the verb built in the first sentence. The patient of a verb is said to be in the absolutive case, which embraces both the direct object of a transitive verb—the temple in the first sentence—as well as the subject of an intransitive verb—the king in the second sentence.

To understand this in terms of English, change the first sentence into a passive form by saying, “The temple was built by the king”. This makes the temple the subject, just like the king in the second sentence; neither one is the agent of any action, but something is happening to them: the temple is built, and the king is drawn into sleep. In an ergative language they are both in the absolutive case, and the distinction between active and passive is lost.

For more details about ergativity see the Wikipedia article. Both Hurrian and Sumerian are ergative, as are some modern languages such as Basque.