When you "ping" somebody to a thread, you place their screen name in the To Line and then you post your reply. If YOU are the pingee you will then get a bold message on your Browse page or latest Posts (top right) saying "New Posts to You". You may click on this bold link and it takes you to your own private comments page where you can see who has pinged you and where you can go to respond to your ping.
Bump means to reply to a post thus "bumping" that post to the top of everyone's latest post page (at leat for the moment) It gives visibility to everyone of your post. So when you reply to THIS message you will have pinged me and everyone else you put in the To box and you will Bump this Black thread to the top of the list.