A casting is a visual interview where the model must present his or herself infront of a client or casting director. Even if a client has seen your pictures they still meet in person to be sure that the pictures are a recent reperesentation of how you currently look and to make sure you skin condition etc. is the same. Also they may want to see you walk or pose as well. There may be time that the casting is with the photographer present to make sure that he is able to work with you.
There are no rule to a casting. It could be a small thing where there is only two or three models or it could be complete frantic such as in New York City when they are casting for the Mercedes Benz Fashion Week (Although it will no longer carry that name anylonger) when the models are running around attending what seems like endless casting with undreseds of other models. You could end up waiting for an hour to see someone for just 4 minutes. You get to the location for casting and sign in. You will wait in a room with 20 other models until its your turn. You walk in where the client is and they ask you a some simple rutine questions. They will most likely take your picture or keep your comp cards and look through your portfolio. If it is for runway, they will ask you to walk for them, or perform a quick couple of poses. Finally, you will say good-bye.
They almost never give a decision right away unless you are Gigi Hadid like here below.