First understand that the connection of "Contacts" is a one-directional. This means when you make someone a Contact of yours, you are not made a Contact of theirs. Knowing this, when you look at a profile and select "Contacts", you are seeing the people they have made their Contacts (connections they have made).
"Contacts of" is the just the opposite. When you select "Contacts of", you will see the list of people that have made the the member their "Contact". These are connections made by each of the people on the list.
Taking that a step further, "popular" members are users who are "Contacts of" many other members.