It's important to understand that each section of a song typically has a role to fulfill. If you know the purpose of each section in your song, you'll be better prepared to write a great song. Of course, most songs won't use all of the sections listed below, but knowing the purpose of your sections is crucial to understanding how to put together a solid song.
Verse
Lyrically, the verses of your song will move your story forward. The chorus or refrain is likely to have the same words each time, so the verse is your chance to keep your ideas moving along.
Chorus
Think of your chorus as the big idea for what your song's all about. That's partly why your title is most likely to show up in your chorus. Your title also sums up what the song's about. Melodically, the chorus will be the catchiest part of your song. This is what people will have stuck in their head long after your song is over. That's another reason it's good to have your title in the chorus. When people get your chorus stuck in their head, they'll easily know what your song is called and can find it later when they want to hear it again.
Pre-Chorus
The pre-chorus is an add-on before the chorus. It usually repeats the same lyrics each time, the same way a chorus does. Musically, a lot of times it creates a nice build up to what's coming in the chorus. Katy Perry's "Firework" was a good example of that, as you saw above.
Bridge
The bridge is a departure from what we've heard in a song, previously. This goes for both the lyrics and the music. Lyrically, it's an opportunity for a new perspective. Musically, it's a chance to offer the listener something they haven't heard before to keep the song interesting.
Refrain
In the verse / verse / bridge / verse song structure, the refrain is the line that draws all the attention in your verses. It's usually at the beginning or end of each verse and is often the title of the song.
Hook
The hook doesn't necessarily refer to a specific section of a song, except to say it's the catchiest part of a song. Most of the time, it will be your chorus, if your song has one. If your song doesn't have a chorus your hook will most likely be your refrain. As hit songwriter, Clay Drayton, says "A fish knows the hook... Once it's in you, it's hard to get it out."