Just like bluexx said.Local switches are for the event in witch they are used.You can have two events close to each other,and both of them turn on local switch A.The first event will turn local switch A on just for himself,as will the second.So if you only turn local switch A on the first event ,the second will still have local switch A off.
Now if its a regular switch,when you turn it on with one event it will be on for every event in that map.
Hope this is somewhat understandable!