but doesn't pinging a computer flood a connnection?
Only when you ping a system to the point where it can no longer function. This can be very difficult on some systems and very easy on others. That's where security comes in. I believe you are referring to Denial of Service attacks. These types of attacks are ment to crash a system operating on the internet by sending it so many requests that the system just gives up or 'crashes.'

A good analogy would be a mailbox sort of...

Think of the letters as packets of data and the mailbox as the computer, the mailbox can only hold so many letters before it explodes.

Hope this helps a bit...

--Peace