October will be an important period for all Office 365 admin because, to provide more security and stability, Microsoft will end the support of legacy technologies.
First of all, after 13 October Office 2013 client will not be supported to connect to Office 365 services and this means that your users can have issues or limitation to use Exchange or Sharepoint.
Office 2016 and Office 2019 client will continue to Office 365 cloud services until October 2023. After that period, only Office 365 ProPlus/Business will be able to use the cloud services.
Up to date information on current system requirements can be found under on the Office system requirements page, with related timelines available in the Office system requirements matrix.
It’s not finished because in the same period there’s will be also the retirement of TLS 1.0 and 1.1 in Office 365, to be replaced with Transport Layer Security (TLS) 1.2+ to provide best-in-class encryption, and to ensure our service is more secure by default. Check your applications or your devices to avoid block or error.