Modality (or "mood," as it's often called) is a way of talking about how the main verbs in a sentence or clause behave. There are four modalities:
Indicative: usually to say something directly; this modality is the most common and is the default
Conditional: usually to show possibility (incl. the future) or necessity / conditional modality is signaled by the use of what is called a modal auxiliary (can/could, will/would, shall/should, may/might, or must) or a semi-modal (ought to, have to, seem to, etc.)
Interrogative: to ask questions
Imperative: to give commands
Modality is the final comment when analyzing a main verb in a sentence or clause (unless you also are talking about active voice and passive voice, in which case voice is the final comment). Consider the following sentence: "I should have gone to the movies yesterday." Here, "should have gone" is the main verb. This main verb is past perfect conditional.
Past (it uses the past form "should" rather than the present form "shall")
Perfect (it uses a HAVE + past participle construction "have have")
Conditional (it uses a modal auxiliary "should").
I'm sure there's more to say, but those are the basics.