Essentially, each subscriber has a key in their smart card. When a new subscriber is added or changes their service, a new group key is sent over the broadcast system, encrypted with that subscriber's key. The keys to actually decrypt individual programs are themselves encrypted with the group key for the set of services that program belongs to. Legitimate subscribers decrypt the program keys using the group keys, which they decrypt using their subscriber keys.
If someone changes their service, change messages are sent over the system. They're repeated at random intervals to make sure someone gets a new service even if their box was off or missed a signal and to make sure someone eventually gets a service removed if they stopped paying for it or request it be removed.
All of this takes place inside the smart card, a physically secure computing system. Typically, the smart cards can be reprogrammed, but the new programming must be signed. To upgrade smart cards, new programming is sent over the satellite and is signed so existing cards accept it. The service provider knows what smart card each subscriber has and can run multiple distinct security systems concurrently, provided everyone who wants to watch the same show, and is allowed to do so, winds up with the same key to decrypt the actual contents.
There are many ways to pirate cards, but typically a number of pirated cards are all clones of a single subscriber. The system is one-way, so it can't tell if a card has been duplicated. When a card is "hit', that means the operator figured out the card was duplicated (often by one such duplicated card falling into its hands). They then de-authorize that subscriber, shutting off all the pirates using that particular subscriber key.
The pirated cards may be smart enough to ignore the de-authorization. But even so, as soon as the group keys are changed, they'll stop working, since they no longer have any way to decrypt the group keys and thus no way to decrypt the keys needed to decrypt the programming.
Sometimes cards are also "hit" by the provider simply changing the logic in the card. The change can be minor, but enough so that the pirated cards become incompatible with the system. This can be either because the pirated cards reject the update and become incompatible because the protocol has changed or it can be because the pirated cards accept the update and cease to be pirated cards. This can affect every pirated card of a particular type in existence, even if they all use different accounts.