A quatrain is simply 4 lines of rhymed poetry. There are 3 main types of Quatrains. In the diagram below, A's are lines that must rhyme with all other A's, and B's are lines that must rhyme with all other B's:
A
A
B
A
A
B
A
B
A
A
B
B
Here are some examples based on the diagrams above:
In the fog
I saw a dog
Barking aloud
Atop a log
My friend is nice
Her name is Ann
And she eats rice
Out of a can
In the winter I sigh
When the flowers die
In the spring I grin
To see them again