Associations is a tap found in the accounts, and contacts window, showing the relations between the different accounts and contacts. 

In the Accounts window's Associations tap you can only see how other accounts relate to the account that you are on. For example you can see which other accounts have the same parent, a.k.a. is a "Sister" account. By double-clicking on an account you go directly to that account's page. New sisters, etc., gets automatically added when a new account gets assigned a parent account. The type of associations does not have to those that you see listed on the picture above, by pressing edit you will gain access to the PickList Editor where you can set up your own list. Read more here.

In the contacts window's Associations tap you can see both how the contact relate to accounts or to other contacts.  

Like the "type" describing the accounts' relationship to the account that you had open, the types in the contacts window can also be custom made by going to the PickList Editor.