An unpredictable person or thing, liable to cause damage if not kept in check by others.

The allusion in the phrase is to improperly secured cannons on ships which were likely to roll about on deck and damage the ship. No evidence has come to light to indicate that the phrase was used by sailors in the days that ships carried cannons. The term is alluded to in Victor Hugo’s novel Ninety Three, 1874. A translation of the French original describes cannons being tossed about onboard following a violent incident onboard ship:

"The carronade, hurled forward by the pitching, dashed into this knot of men, and crushed four at the first blow; then, flung back and shot out anew by the rolling, it cut in two a fifth poor fellow" ...

" The enormous cannon was left alone. She was given up to herself. She was her own mistress, and mistress of the vessel. She could do what she willed with both."

Henry Kingsley picked up this reference in his novel Number Seventeen, 1875 :

"At once, of course, the ship was in the trough of the sea, a more fearfully dangerous engine of destruction than Mr. Victor Hugo’s celebrated loose cannon."

The earliest figurative use of 'loose cannon', i.e. a usage not relating to actual cannons, in print that I can find is from The Galveston Daily News, December 1889:

The negro vote in the south is a unit now mainly because it is opposed by the combined white vote. It would in no event become, as Mr. Grady once said, "a loose cannon in a storm-tossed ship."