A nominative-absolutive language is one where the only argument of an intransitive verb (that is, the subject) is marked sometimes in the same way as the subject of a transitive verb, and some other times in the same way as the direct object of a transitive verb. Thus, the marking of the intransitive subject, often called experiencer or S, varies according to certain criteria defined by each given language. The criteria tend to be based of the degree of volition or control of the verbal action by the subject.
For most languages of this type, the marking of the intransitive subject is fixed for each verb, regardless of the actual degree of volition of the subject, but often corresponding to the most common occasions. For example, the subject of swim is always nominative (agent-like), and the subject of sleep is always absolutive (patient-like). In a language like this, if the subject of a verb like swallow is nominative, it will be always so, even the action of swallowing is involuntary. This subtype is known as split-S.
In a few other languages, the marking of the intransitive subject is decided by the speaker "on the spot" based on semantic considerations. That is, for any given intransitive verb the speaker may choose whether to mark the subject as nominative or absolutive, with nominative marking implying a degree of volition (agent-like behaviour), and absolutive implying lack of volition or control. This subtype is known as fluid-S.
If the language has morphological case, then the arguments of a transitive verb are marked using the nominative case for the subject and the absolutive case for the object, while the argument of an intransitive verb is marked as nominative or absolutive.
Languages lacking case inflections may indicate case with different word orders. For example, an absolutive argument might precede the verb, while the nominative argument might follow.
Other widely used terms for these kinds of systems are active language and agentive language. The grammatical relations can be called agentive case (corresponding to nominative above) and patientive case (absolutive).