There’s nothing wrong with what Office Web Apps offered, and it doesn’t appear that much of anything has changed with the new Office Online name, but it’s clear that people weren’t using the service as much as Microsoft would like.
“First, we’re renaming Office Web Apps to Office Online so you know where to find our free online experience. We heard from customers that the inclusion of Apps in our name was confusing,” writes Microsoft’s Amanda Lefebvre. “Secondly, a lot of you don’t know that we have an online version of Office because you just couldn’t find it.”
The rest of the post is essentially instructions for how to locate the service along with a description of what it is. For the record, Office Online is exactly what you think it is--an effective combination of Microsoft Office features (but free!) and the cloud-stored, real-time collaboration capabilities that the likes of Google Drive offers.
You can use the free online versions of Microsoft Office applications by visiting Office.com and logging in with your Microsoft account.