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:
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:
Now treat this entire segment as a unit, and repeat it. In pop music, this is the second verse:
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:
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.