As Motoko11 explained why clients are whitelisted, I notice no explanation of what whitelist is. A whitelist is basically the opposite of a blacklist.
A blacklist is a list of things NOT allowed for something, example a list of people not allowed in America, they will be refused access at airports.
In the case of BakaBT and whitelisted torrent clients, because there are FAR too many clients and more cropping up everyday, it is simpler to create a list of "allowed" clients, rather than disallowing each and every single new one that appears.
In other words, a whitelist, is a list of what can be used/is allowed. Anything not on that list, is ignored/denied permission to do it's purpose.