It has web applications, but they do not replace the desktop ones feature-wise. When you buy Office 365 subscription, you get both web access and desktop apps.
If you use OneDrive, then you basically get just the web apps for documents stored in there (which is also the easiest way to check out).
There's a "light" version available online, but you must be thinking about Office 365.
Although the core product is still desktop based, they've been shifting to an optional subscription model where you pay $9/month or so for perpetual updates and 1tb of storage.
This model is great for me. It's very rare that I need to view or edit a document in an Office application but it does happen occasionally when the formatting is complex or something. Just install Office in a VM, pay $9 for 1 month of access, and unsub again when I'm done!
Microsoft Access is still used pretty heavily. As a developer, you may at some point be handed off an Access database. Additionally, Powerpoint still gets heavy usage, and switching to Google's version you're likely to lose a lot of design fidelity.