Java Networking: Explain InputStream and OutputStream in Socket

I have created a server by using ServerSocket. After that, I have created Client using Socket, and connect to this server.

After that, I do "some stuff" with InputStream and OutputStream is taken from Socket Object. But, I don't really understand inputStream and outputStream so much. Here is my simple code :

private Socket sock = null;
private InputStream sockInput = null;
private OutputStream sockOutput = null;

...
            String msg = "Hello World";
            byte[] buffer = null;

            try {
                sockOutput.write(msg.getBytes(), 0, test.length());
                sockOutput.write("Hello StackOverFlow".getBytes(), 0, test.length());
                buffer = new byte[test.length()];
                sockInput.read(buffer, 0, test.length());
                System.out.println(new String(buffer));
                sockInput.read(buffer, 0, test.length());
                System.out.println(new String(buffer));
            } catch (IOException e1) {
                e1.printStackTrace();
                }

The result will be : "Hello World" and "Hello StackOverFlow".

Here is server side code :

private int serverPort = 0;
    private ServerSocket serverSock = null;

    public VerySimpleServer(int serverPort) {
        this.serverPort = serverPort;

        try {
            serverSock = new ServerSocket(this.serverPort);
        }
        catch (IOException e){
            e.printStackTrace(System.err);
        }
    }

    // All this method does is wait for some bytes from the
    // connection, read them, then write them back again, until the
    // socket is closed from the other side.
    public void handleConnection(InputStream sockInput, OutputStream sockOutput) {
        while(true) {
            byte[] buf=new byte[1024];
            int bytes_read = 0;
            try {
                // This call to read() will wait forever, until the
                // program on the other side either sends some data,
                // or closes the socket.
                bytes_read = sockInput.read(buf, 0, buf.length);

                // If the socket is closed, sockInput.read() will return -1.
                if(bytes_read < 0) {
                    System.err.println("Server: Tried to read from socket, read() returned < 0,  Closing socket.");
                    return;
                }
                System.err.println("Server: Received "+bytes_read
                                   +" bytes, sending them back to client, data="
                                   +(new String(buf, 0, bytes_read)));
                sockOutput.write(buf, 0, bytes_read);
                // This call to flush() is optional - we're saying go
                // ahead and send the data now instead of buffering
                // it.
                sockOutput.flush();
            }
            catch (Exception e){
                System.err.println("Exception reading from/writing to socket, e="+e);
                e.printStackTrace(System.err);
                return;
            }
        }

    }

    public void waitForConnections() {
        Socket sock = null;
        InputStream sockInput = null;
        OutputStream sockOutput = null;
        while (true) {
            try {
                // This method call, accept(), blocks and waits
                // (forever if necessary) until some other program
                // opens a socket connection to our server.  When some
                // other program opens a connection to our server,
                // accept() creates a new socket to represent that
                // connection and returns.
                sock = serverSock.accept();
                System.err.println("Server : Have accepted new socket.");

                // From this point on, no new socket connections can
                // be made to our server until we call accept() again.

                sockInput = sock.getInputStream();
                sockOutput = sock.getOutputStream();
            }
            catch (IOException e){
                e.printStackTrace(System.err);
            }

            // Do something with the socket - read bytes from the
            // socket and write them back to the socket until the
            // other side closes the connection.
            handleConnection(sockInput, sockOutput);

            // Now we close the socket.
            try {
                System.err.println("Closing socket.");
                sock.close();
            }
            catch (Exception e){
                System.err.println("Exception while closing socket.");
                e.printStackTrace(System.err);
            }

            System.err.println("Finished with socket, waiting for next connection.");
        }
    }

    public static void main(String argv[]) {
        int port = 54321;
        VerySimpleServer server = new VerySimpleServer(port);
        server.waitForConnections();
    }

My question is :

1. When I use sockOutput.write and I can get back those message back by sockInput.read. So, those message has been saved, right? If this true, does it saved on Server I have created or just saved in some other thing such as Socket Object.

2. If I have written to socket String A1, A2,... An so I will receive A1, A2, ... An String respectively, right?