"ad hominem" is a Latin phrase used very commonly in English (just like "ad nauseum", and also "i.e." and "e.g." are abbreviations of Latin phrases). It is, effectively, part of English.
What it means is, in the context of an argument, referring to who made the argument, as opposed to the argument's own referents, in deciding whether to accept or reject it. It is normally considered proof that one has no real argument to offer against what is said, if one must invoke "who wrote it" as an refutation.
Ad hominem delete is a more abusive form of ad hominem revert which makes the text invisible (to all but sysops in mediawiki), makes it impossible to retrieve older versions even if the most recent version is found and restored by the author or others, and most importantly, makes the text not part of the XML dump. What is worse, this does not even show up on the watchlists of those who are watching the article! Very bad idea.
It is applied with amazing regularity on Disinfopedia and Meta-Wikipedia and to some degree at Consumerium in the R&D phase. It is applied also with regularity at Wikipedia but only by certain people - who employ it as a deliberate power grab by the sysop power structure to make it difficult for those who disagree with it, or the GodKing to communicate even the most essential concepts to the end user... suggesting very strongly that political disputes underlie all such deletes.
Because of the suspicious circumstances and regular abuse of deletes, most large public wikis run a deletion log to record what has been deleted, and a pending deletions or votes for deletion page to debate what may be deleted. This is true even on those wikis (like Disinfopedia) where a small unaccountable clique over-rides such debates and does surprise deletes on heavily-linked articles - so there's clearly some intent to move to some more accountable power structure long term even if they don't have it just yet.
The use of delete, like block IP, is a major governance issue. It tends to make a big difference in how troll-friendly a wiki is, and how predictable the service is that is provided to its end users. For the Consumerium buying signal, this is quite important, and surprise deletes will almost certainly annoy some faction if some approve of it and some not.