Verses do 'exposition', 'exposing' the Storyline, setting the scene, putting 'props' on the stage, introducing Characters, like the Singer-Character, the Love-Interest Character, the 'Conflict-Character' (other man, other woman, in a love triangle). 
The Singer-Character explains his/her 'situation', expressing their satisfaction or complaint about it.

A Chorus sums up. It expresses the main idea of the Storyline, the gist of the Singer-Character's point of view (satisfaction, complaint).

If a Verse III can be found to satisfactorily end the Storyline, a denouement, that enables a final giving of the Chorus.
If a satisfactory Verse III can't be found, writers resort to a Bridge, a Stanza with its own Melody, different from either the Verse or the Chorus, brief, ideally with pivotal Lyrical information relevant to the Storyline, which enables the final giving of the Chorus. 

Song-Writers sometimes write a Pre-Chorus of many Lines, like a Stanza unto itself.
A Pre-Chorus need only be brief, a 'lift' of Melody or emotional urgency in Lines at the end of a Verse, indicating that it is time for the Chorus.
Some Songs can start with the Chorus. Structure depends on what works. If it works it works. If it doesn't work, it doesn't work. Exploring possible Structures can change your Song-Writing, to add variety to your Songs.
Rhyme Schemes can vary. The four-Line Verse I, Rhyming Lines 1 and 3, 2 and 4, gets boring if every Song uses that Structure.
Nursery Rhymes use a Structure Rhyming Lines 1 and 2, and then leaving Line 3 hanging, un-Rhymed.
A 3-Line Verse II typically Rhymes Lines 1 and 2, and picks up the un-Rhymed Line from Verse I, Rhyming in in Verse II, Line 3.
It has the effect of internal Rhyme, adding to Rhythm, the 'beat' of the Melody as sung. 

Word choices are important in engaging listener interest, 'Hooking' them into paying attention. 
Are they engaged by visual images, familiar situations, abstract concepts, concrete concepts?
What 'Hooks' you in your favorite Songs? What Songs fail to 'hook' you? A little study can be very educational.
Each sound has 'Hook Factor'. The Introductory Movement serves that function, supplies that demand, Hooking listener interest, keeping them Hooked until the Vocal Melody takes over, supplying Hook Factor with the Timbre of the voice, the sense of the Singer-Character, the Lyrical concepts. 
The increased emotional urgency of the Pre-Chorus 'lift' and the Chorus delivery sustains the Hook-Factor. Or, doesn't. 
The number one complaint of Publishers is that a Song's Chorus sounds too much like the Verse. It doesn't increase in emotional urgency. It might use the identical Notes of the Verse, the same tempo, the same Melody, and the writer never noticed because they never studied the Songs they think do it right, and the Songs they thing do it wrong.
People have been writing Songs for thousands of years. Some Songs become classics, for a reason. Study the classics to see if you can perceive why they became classics. Thousands of other Songs didn't become classics. Study some one-hit-wonders, and see if there's a perceptible reason why they didn't.