PM means Personal Message. It is a message in chat, where only the person whom you sent pm can view/read it and no one other than that person. It's like sending messages in chat only to a particular person, instead of making it public.
You may send someone pm by typing '/pm' and then a the person's name whom you want to pm and finally the message you want to send. For example, if you want to pm Petrarca and say hello, then you are to put it in this format-
/pm Petrarca Hello!
It's simple as that and I guess if you had read the chat page, you would have saved your time asking how it is done.
While sending a PM (Personal Message or Private Message) is a chat term I have seen a few people seemingly using the same term in reference to the site messaging system, but the true meaning is chat based only.