If you are looking for information about the old "contact linking" feature, see Show Contact Linking fields in Outlook.
Outlook 2013 introduced a neat feature where all contacts for a person are linked together and the aggregate data from all of the linked contacts is displayed on a contact card, with the source of the data listed on the contact card. You can click a link to open any one of the contacts associated with the person.
Outlook does a pretty good job at matching the contacts but occasionally gets it wrong. When contacts are incorrectly linked, or not linked, you can correct the links from the contact card. (You can't bulk unlink all contacts.)
Under list of associated contacts (View Source) is a link for Link Contacts. Click this link to open the Linked Contacts dialog shown here.
To unlink contacts, hover a name then click the X beside the name to unlink it from the contact.
To link contacts, type a name into the Search field to search for Contacts to link to the contact. Select the names you want to link to the contact.
Disable this feature
If you hate this feature, you can't (yet) disable it. Make sure you vote for the ability to disable it in this thread at Outlook UserVoice (and leave a comment telling Microsoft why it's important.)
Adding an option to disable the Contact Linking feature (Outlook Uservoice)