Surname of one of the old noble families in Ankh-Morpork, the most powerful city-state on the Sto Plains. The Selachii family cordially detest the Venturi family, and vice versa. Put another way, the two families hate each other but, as befits noblemen, are extremely polite about it. They do carry on conversations with each other when they happen to meet at parties, and so that they do not embarrass themselves, they only talk of extremely non-controversial subjects. The Selachii men are usually Assassins, that is, not only acquiring the classical education at the Assassins' Guild, but actually practising.
Currently, Lord Robert Selachii is a licensed and active Assassin. (He was retained to inhume The Band With Rocks In, but had to abandon the contract due to their unusual protection.) Lady Selachii, however, is the family leader when it comes to throwing parties and acknowledging dubious heirs to old titles. Known past members of the family include: the famous assassin Sir Bernard Selachii and Lord Albert Selachii, who lived back in the times of Lord Winder and Mad Lord Snapcase.
In Hogfather, a rocking horse coveted by the young Alberto Malich was reserved for Lord Selachii. Given that Albert (as he later became) was born some 2,000 years prior to current Discworld events, the Selachiis clearly have a very long pedigree.
On a side note, given that "Selachii" is the Latin term used by biologists to refer to the shark family (and a venturi being part of most jet engines), it seems reasonable to postulate that some comparison with Bernstein's two warring teen groups, the Sharks and Jets of West Side Story, is intended in the names of Ankh-Morpork's two rival families. This is further borne out by their comparison, in Wyrd Sisters, with the two antagonist groups in Shakespeare's Romeo and Juliet, the Montagues and Capulets, who of course formed the basis for the idea of the Sharks and Jets.
It is also worth noting that a remora is a sort of parasite fish that uses a sucker mouth ringed with teeth to latch onto a shark's hide and share the ride plus any nutrients it ingests. Once attached, a Remora is a Shark's friend for life. Or, alternately phrased, a Shark is a Remora's meal-ticket for life.