A linked contact is a contact who appears in multiple follow-up periods. If you have migrated an individual contact from a previous period, you will see a note on their personal page with the previous periods. The note will look like like this:
Creating linked contacts allows you to keep track of the same contact across follow-up periods. The contact keeps the contact information from the previous period, but otherwise gets a clean slate for follow-up progress (e.g. events attended, connection status). Note that the contact will count as part of the analytics for both the active period and previous ones.