Go to Audience > Contacts.
Search for and select the contact email address or mobile number, or select the Edit icon.
The date of their most recent subscription is displayed in the top left of the Overview tab.
Read more in Single customer view.
If a contact unsubscribes and then resubscribes, the date of the most recent resubscribe is shown.
Contacts subscribed prior to 15 October 2014 always display Unknown.