In most cases, 'Next Renewal' and 'Final Renewal' refer to the same date, i.e. when an account's subscription ends. However, when there is more than one subscription, these dates will differ.
For example, if the main subscription expires on December 2018, but the add-on subscription ends on October 2018, and today is August 2018 then:
'Next Renewal' refers to October 2018 because it is the soonest date.
'Final Renewal' refers to December 2018 because it is the latest date.
If today is November 2018, then 'Next Renewal' and 'Final Renewal' both refer to December 2018 because it is the soonest and latest date.
If today is January 2019, then 'Next Renewal' will be empty because there is no new subscription end date.
'Final Renewal' will remain December 2018 because it was the last date the account was subscribed to you. If the account doesn't renew, this is equivalent to the date they churned.