If you have your activity history synced across your devices through your Microsoft account (MSA), you will no longer have the option to upload new activity in Timeline. AAD-connected accounts won’t be impacted. To view web history, Edge and other browsers have the option to look back at recent web activities. You can also view recently used files using OneDrive and Office.
Microsoft has since updated the post to clarify that Timeline and the associated activity history will still be a part of Windows 10, but if you're using a Microsoft account it will only be available locally on that machine. It's not entirely clear what is behind the change, but as Thurrott points out, it also lost Android syncing late last year when Microsoft killed its launcher on the platform, so the potential for doom remains high.
If you're not in the Insider beta program, a Microsoft support page mentions that cross-device syncing will go away for you in June, so anyone who uses it has a few months to prepare. Timeline was the "star" of Microsoft's fall 2018 update for Windows 10 (after a delay pulled it out of the earlier Creators Update) and while it will still remember everything you did, it just won't save that information to the cloud anymore.