Latin Grammar: The Supine

I. Cases
II. Uses
III. Importance
IV. The Supine with iri

I. Cases

Accusative case: 4th principal part with -um ending (Ex: portatum, doctum, dictum, captum, auditum)
Ablative case: 4th principal part with -u ending (Ex: portatu, doctu, dictu, captu, auditu)

II. Uses

Accusative case: used with verbs to express the purpose of a movement (Ex: pueri exercitum cucurrerunt | The boys ran in order to practice)
Ablative case: used with particular adjectives (Ex: Mirabile dictu! | Wondrous to say!)

III. Importance

Supines help in listing the principal parts of a verb. The principal parts of a verb are listed as follows: (the first person singular present form of the verb), (the infinitive of the verb), (the first person singular perfect form of the verb), (the supine of the verb). (Ex: "to order": iubeo, iubere, iussi, iussum | 'iussum' is the supine of this verb)

IV. The Supine with iri

The accusative supine can be used with iri to form a future passive infinitive. (Ex: pater dicit domum factum iri | The father says that the home will be built)

Sources: A Student's Latin Grammar, Cambridge University Press. This book is great.