Broken square

A broken square refers to an infantry square collapsing or breaking up in battle.
Specific incidents that this expression may refer to are all in the Mahdist War in the Sudan:
After the Mahdist War, the poet Sir Henry Newbolt got his information very wrong (and may have confused these two battles with each other) and wrote a poem named "Vitaï Lampada" describing a disastrous collapse. Or he may have intended to write a fictional "worst case" scenario, with the message "even if the worst happens, keep on fighting back", but many readers thought wrongly that he was describing real events.
Frank Richards, a soldier in the Royal Welch Fusiliers around 1901, stated in his memoir entitled 'Soldier Sahib': "If a Welshman went into a pub where a Highland soldier was, of the regiment whose square was once broken by the Mahdi's dervishes in the Sudan, he would sometimes ask for a 'pint of broken-square'. Then he would have his bellyful of scrapping for the rest of the night, because this was an insult the Highlanders could not forgive." Robert Graves, who also served in the Royal Welch, told a similar story. 
In Spain in the Napoleonic War, at the Battle of García Hernández, three French squares were broken in the same day resulting in a very one sided victory for the British and Germans.
For more information about infantry squares breaking or not breaking, see Battle of García Hernández#Commentary.
In the Napoleonic Wars, when cavalry broke an infantry square, it was usually because one of more of:
See also.
Fuzzy-Wuzzy.