When you have finished your session, you should log out by typing the server's own logout command. This might vary between servers; if in doubt, try logout or exit, or consult a manual or your system administrator. When the server processes your logout command, the PuTTY window should close itself automatically.
You can close a PuTTY session using the Close button in the window border, but this might confuse the server - a bit like hanging up a telephone unexpectedly in the middle of a conversation. We recommend you do not do this unless the server has stopped responding to you and you cannot close the window any other way.