Jenkins is captain of a ship named the Milka, with which he runs various nefarious cargoes in and out of any port he can. His boat has smuggling compartments and a notorious crew, including his first mate Mr Scoplett. Jenkins has his comeuppance when he tangles with Commander Sam Vimes, who takes command of his boat, strips it of everything weighty (including lifeboats, anchors, cargo...) and chases after 71-hour Ahmed in it.
The captain is renowned for carrying cargoes that are a bit off - cabbages full of caterpillars, offal going a bit green, that sort of thing. However, he probably took it a bit too far when he was caught taking a hold full of crossbows to Klatch during the build-up to war in Jingo.
Jenkins may have recived his name from Robert Jenkins, whose ship was boarded by the Spanish Coastguard 1731 and resulted in the cutting off of Jenkins ear after an accusation of piracy. The incident was used as a casus belli in 1738 to justify the war between England and Spain most commonly known as the War of Jenkins' Ear.