Songs at the most basic level are structured by verse. Most contempory songs add a chorus. A bridge, although not as popular can also be added. In addition songs can also contain: an intro, a pre chorus (also called a build), a refrain and an extro (also called an outro or tag).
A brief explanation of the different song sections:
Verses are structured lines that while differ in content follow the same musical pattern.
A chorus differs both musically and lyrically from the verse and is repeated at least once in the song.
A bridge differs both musically and lyrically from the verse and the chorus. Usually only used once in the song.
A refrain is one or two lines at the end of each verse which while different lyrically from the verse remain consistent to themselves.
The into is a different musical form that comes at the beginning of the song. It differs from the verses but can and often does share music and or lyrics with the chorus.
Pre Chorus (also called a build):
A pre chorus precedes the chorus. While keeping the same music form the pre chorus can lyrically change throughout the song. It is usually repeated as often as the chorus.
Extro (also called Outro or Tag):
Stylistically the same as the intro, except it occurs at the end of the song.
The different forms
The Traditional AAA form.
The AAA song form consists only of verses. Sounds simple but it is one of the harder forms to write. Both words and melody must be fresh and compelling, there is not chorus or bridge to break things up.
The ABA form.
(A = verse, B = chorus)
The ABA form adds a chorus. More often you will see it as ABABA or AABABA. This fits in well with modern pop music. Adding a chorus allows the songwriter to move the song in a different directon musically. Lyrically, the chorus is the meat of the song, usually repeating the title while summing up what the song is about.
The ABCA form.
(A = verse, B = chorus, C = bridge)
Also quite popular the ABCA form adds a bridge. The verse and chorus have the same function as the ABA form. The bridge can be used lyrically to clear up parts of the song that may otherwise be obscure. Or to tie the song together, hence the name bridge. Musically a bridge is used to break up a pattern that may be getting a little too monotonous or predictable.
There are other forms of course, these are the most common. What form you use depends a lot on what musical genre you are wrting your song in.