Welcome to AC.
Connections just join the same person together (so you can have the same person as a Google contact, a Facebook contact, a Skype contact, a work email contact, etc). That way he shows up as a single person/contact on your phone instead of several.
For example,on mine I have a contact with connections like this:
So he's a Google Contact, but I have him joined to two things (Exchange/Work is the square on the left, and I also have him as a Skype contact).
If you click on the connections section, it should open up and tell you what the connections are or what the icons mean.