This means that the first and third lines of each stanza rhyme, and the second and fourth lines rhyme.
For example, the first stanza is:
> The old priest Peter Gilligan
> Was weary night and day;
> He travelled over bog and ban,
> To preach the Gospel word, say.
Here, "Gilligan" rhymes with "ban" and "day" rhymes with "say". This pattern continues throughout the entire poem.