A Balliol rhyme is a doggerel

Doggerel

Doggerel is a derogatory term for verse considered of little literary value. The word probably derived from dog, suggesting either ugliness, puppyish clumsiness, or unpalatability in the 1630s.-Variants:...

 verse form with a distinctive meter. They are quatrains consisting of two pairs of rhyming couplets, each line having four beats. The first couplet contains the name of a particular individual, and the second couplet usually elaborates on that person's character or exploits or weakness.

The form is associated with Balliol College, Oxford

Balliol College, Oxford

Balliol College , founded in 1263, is one of the constituent colleges of the University of Oxford in England but founded by a family with strong Scottish connections....

. It originated with "The Masque of B-ll--l", published anonymously by a group of Balliol undergraduates in 1875. The verses were inspired by the conventions of traditional mummers plays

Mummers Play

Mummers Plays are seasonal folk plays performed by troupes of actors known as mummers or guisers , originally from England , but later in other parts of the world...

 (at their peak of popularity in the late 19th century), in which the dialogue took the form of simple verses, and in which characters introduced themselves on first entrance with some such formula as: "Here comes I a Turkish Knight / Come from the Turkish land to fight".

Balliol rhymes are almost always about a person. They are not to be confused with Clerihew

Clerihew

A clerihew is a whimsical, four-line biographical poem invented by Edmund Clerihew Bentley. One of his best known is this :* It is biographical and usually whimsical, showing the subject from an unusual point of view; it pokes fun at mostly famous people...

s.

Examples

About Benjamin Jowett

Benjamin Jowett

Benjamin Jowett was renowned as an influential tutor and administrative reformer in the University of Oxford, a theologian and translator of Plato. He was Master of Balliol College, Oxford.-Early career:...

, Master of Balliol (from "The Masque of B-ll--l"):

First come I. My name is J-w-tt.

There's no knowledge but I know it.

I am Master of this College,

What I don't know isn't knowledge.

About George Nathaniel Curzon

George Curzon, 1st Marquess Curzon of Kedleston

George Nathaniel Curzon, 1st Marquess Curzon of Kedleston, KG, GCSI, GCIE, PC , known as The Lord Curzon of Kedleston between 1898 and 1911 and as The Earl Curzon of Kedleston between 1911 and 1921, was a British Conservative statesman who was Viceroy of India and Foreign Secretary...

:

My name is George Nathaniel Curzon,

I am a most superior person.

My cheeks are pink, my hair is sleek,

I dine at Blenheim

Blenheim Palace

Blenheim Palace  is a monumental country house situated in Woodstock, Oxfordshire, England, residence of the dukes of Marlborough. It is the only non-royal non-episcopal country house in England to hold the title of palace. The palace, one of England's largest houses, was built between...

 twice a week.

About the building of the Athenaeum Club

Athenaeum Club, London

The Athenaeum Club, usually just referred to as the Athenaeum, is a notable London club with its Clubhouse located at 107 Pall Mall, London, England, at the corner of Waterloo Place....

 (it does not follow the AABB rhyme scheme):

I'm John Wilson Croker

John Wilson Croker

John Wilson Croker was an Irish statesman and author.He was born at Galway, the only son of John Croker, the surveyor-general of customs and excise in Ireland. He was educated at Trinity College, Dublin, where he graduated in 1800...

,

I do as I please;

Instead of an Ice House

I give you - a frieze!