Breed Specific Legislation is a law that restricts a certain breed or breeds (Almost like the segregation laws, only directed toward dog breeds) and can be directed toward any breed, but most commonly the Pit Bull Terrier. It can put a lot of restrictions to owning a breed, but in most cases, it just completely bans the breed or breeds all together.
Legislators think that by eliminating an entire breed of dog, all of the problems with dogs attacking people will go away and bring a "safe community" into the picture. This doesn't work because it doesn't take care of the root of the problem and studies have shown that it doesn't even reduce the number of dog bites. Dogs that belong to irresponsible and mean people will almost always turn out to be an irresponsible and mean dog, regardless of the breed. therefore, BSL tends to "punish the BREED, not the DEED" and forces punishment onto thousands, possibly millions, of great dogs and owners along with the one or two bad dog(s) and owner(s).
Another problem with BSL is that there are over 100 breeds of dogs that are popularly misidentified as a pit bull, one of which is a Fila. I have personally owned a Fila that came to my house as a stray and I took him in. His temperament wasn't the best (I assume the previous owner was a dead beat), and everyone that saw him immediately asked, "Is that a pit bull?" When I answered no, they would respond something to the effect of oh, I thought he was because he was growling at me and he looks mean.
The third problem with BSL is the cost. Most shelters are under funded and under staffed. When BSL is added, more tax dollars have to be pumped into these shelters to "humanly euthanize" these dogs that have done nothing wrong. I can think of a million better ways to waste our tax dollars other than on punishing all of the good, responsible pit bull owners.
A few things you can do to help fight BSL are to communicate your thoughts to any and all politicians that you can find to listen, attend town hall meetings, sign petitions, post flyers with facts about BSL and pit bulls, and so on and so fourth.