How we change what others think, feel, believe and do
A character makes a speech of some kind or otherwise talks for an extended period.
The person they talk to may be visible or not. They may also talk to the reader or to themselves.
The monologue may explain how a person is thinking about a particular topic or may give a broad background to the story (or anywhere in between).
The monologue may be embedded in the story, such as when a person makes a speech, or may be directed at the reader (especially if the point of view of the author is first person).
A person meets a friend they have not met for a long time and tells them what has been happening.
A politician makes a speech about the state of the nation and the world.
Monologues allow things to be said that would be difficult to portray in the normal dramatic frame and thus are a useful device for theatrical and cinematic productions, where the narrative descriptions written in books is not possible.
Classic dramatists such as William Shakespeare make great use of monologues, perhaps more so than modern productions, where actions are often used to speak louder than words.
An exterior monologue occurs where the character speaks to someone off-stage or off-camera.
An interior monologue is where the character speaks to themself.
A soliloquy is where the actor speaks the monologue whilst alone on stage.
A dramatic monologue occurs in poetry, where the poem is from the person of a speaker who talks directly to the reader.
A comic monologue is often a solo speech by a stand-up comic designed to contain a high ratio of humor to words.
Note that a dialogue does not mean a conversation between two people -- the term comes from the Greek 'dia logos', meaning through words.