The verse-chorus (sometimes with a bridge) form replaced the AABA 32-bar formula in popular music at around the sixties.
And the 32-bar form replaced the strophic form (verses sometimes with a refrain) which most earlier folk songs were based on.
So it represents the current taste and is by no means timeless or universal, just a current tendency.
But repetition has been a part of music since as far back in history as we can see.
In order to not be bored, we need surprises.
Surprise implies unexpectedness.
Without expectation there can be no surprise.
Repetition builds expectation, contrast breaks it and provides the surprise.
Unsurprisingly, form in music is based on these two elements: Repetition and contrast.
Of course, with current popular music, since you know where exactly the bridge (contrasting section) will start, there is barely any surprise now, hence the boredom.
music.stackexchange.com/users/10708/cyco130
Someone said that music is about the balance between surprise and the familiar.
This balance is different for different people, some people want to hear new things all the time, while other want the same thing over and over.
The popularity of the structure in the question is likely due to that it's a balance that many people find pleasing.
If you find this formula boring, there sure is tons of music out there which do not follow this pattern.
music.stackexchange.com/users/8682/Meaningful Username
Songs could be looked upon as poetry set to music.
Poems traditionally consist of verses.
Actually far more verses and few choruses, compared with songs.
Familiarity is one of the reasons.
The 'hook' - the catchy bit, is what lots of folk remember, and they like to be able to sing/hum/whistle along with it.
It's often in the chorus, and if it only came once or twice, folks wouldn't have much chance to join in.
Also, repetition is the name of the game with a lot of pop songs, so get in as many repeats as possible !
If the song was verse-verse-verse, or chorus-chorus-chorus, it would be even more tedious.
Thus the format so many songs use.
It does work - having been proved over decades.
If it ain't broke...
music.stackexchange.com/users/2808/Tim
Familiarity is comforting.
Screw with convention too much and many people get uncomfortable.
Even an avant garde songwriter sometimes wants to make some parts of a song familiar and comfortable.
If I want to wow you with words and melody, I don't want to distract you too much from those with strikingly original structure.
And yet, novelty is exciting.
And that's why although this structure is common, it's by no means universal.
If I had asked your question, I would probably have written that the "kind of boring" familiar structure is: verse 1/verse2/chorus/verse3/bridge/chorus ...
and of course there's plenty more variations, even in the most mainstream pop (I'm always struck by how Biology by Girls Aloud has no verses and about 4 different choruses...)
music.stackexchange.com/users/1252/slim
As cyco130 notes, this structure is based on alternating repetition and contrast.
Interestingly, the Classical Sonata-Allegro form is built in almost exactly the same way as the verse-chorus-bridge form, although the expectations for what each section contains are a bit different.
Start with some complete melodic phrase.
In pop music, this is the verse, in a sonata, it is your main theme: A Now add a contrasting phrase.
In pop music, this is the chorus, which tends to be more energetic than the verse.
In classical music, this is the secondary theme, which is usually in a related key, such as the dominant, and often tends to be more relaxed: AB Now treat this entire segment as a unit, and repeat it.
In pop music, this is the second verse: |:AB:| Now add another contrasting section.
In pop music, this is the bridge, which often modulates to a different key, and introduces new ideas.
In classical music, it is called the Development section, which introduces new permutations of previous ideas, and also typically modulates to more distant keys:
|:AB:| C
Finally, add some more repetition.
In pop music, depending on the song and the lyrics, this can either be a full 3rd verse and chorus, or just the chorus (possibly repeated multiple times).
In classical music, this is the Recapitulation section, which doesn't modulate: |:AB:| C AB ||
Finally, pop music might tag on a couple repeats of the chorus with a fade out, where classical music might tag on a Coda.
music.stackexchange.com/users/10637/Caleb Hines
Doesn't matter if it's Rage Against The Machine or Britney Spears song structures are always the same. It always goes something like:  Verse/Chorus/Verse 2/Chorus/Verse 3/Bridge/Chorus .  Why?  Why is this such an accepted structure?  What's the  draw  behind this kind of structure?  (I personally find the repetition kind of  boring  but it seems to be universally accepted.)  Maybe this belongs on psychology SE instead...
Song Structure: What's up with Verse/Chorus/Verse 2/Chorus/Verse 3/Bridge/Chorus?
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music.stackexchange.com/questions/21960
music.stackexchange.com/users/10536/Mo.
S2: The popularity of the Verse/Chorus/Verse 2/Chorus/Verse 3/Bridge/Chorus structure is likely due to that it's a balance that many people find pleasing.   The popularity of this structure is probably due to the fact that it provides people with a pleasing balance.
The popularity of this structure is probably due to the fact that it provides people with a pleasing balance.