Sarah Josepha Hale's rhyme tells a small, real story rather than just chanting nonsense syllables, which gives a one-year-old something to follow: a lamb, a school, a rule broken, a teacher's kind explanation at the end. The steady, singable metre makes it easy to repeat back.
From Mother Goose / Nursery Rhymes (traditional). See the whole collection.
Mary had a little lamb with fleece as white as snow,
And everywhere that Mary went the lamb was sure to go.
It followed her to school one day, that was against the rule.
It made the children laugh and play, to see a lamb at school.
And so the teacher turned it out, but still it lingered near,
And waited patiently about till Mary did appear.
"Why does the lamb love Mary so," the eager children cry,
"Why, Mary loves the lamb, you know!" the teacher did reply.
Public domain. Text from The Little Mother Goose (illustrated by Jessie Willcox Smith, 1912), via Project Gutenberg. View the source edition