Let's imagine that stanza above is our 1 st verse of your song. The reason it would be AAAA is that each line ended with a word that rhymed in following lines. The A refers to the 1 st rhymed line. An X would be used if the line did not rhyme to any other line. Often each line does not rhyme to every other line in a stanza, but maybe to just one or two others.
B represents the second rhymed line.
In a stanza there are sometimes more sets of rhymes that would be referred to as C, D, etc. So, if you look above, you see again that ABAB means that the 1 st and 3 rd line rhyme to each other and the 2 nd and 4 th line rhyme to each other. If the format were AABB, then the 1 st two lines would rhyme and the 3 rd and 4 th line would rhyme. Consider now the stanza below that has lines that do not rhyme. In this stanza, just lines 2 and 4 rhyme.