If you choose to sync your Google Docs locally, any document you've previously worked on will appear in your Google Drive folder. This currently doesn't appear to take up any of your 5GB of space, though Google isn't entirely clear on this point.
If you attempt to double-click on one of these files, it will automatically launch the document on the Web, where you can edit, share, and save it. (Supposedly, you can also enable an offline working mode from within the Chrome browser, but I wasn't able to get it to work when I tried.)
Like Dropbox, you can sync other file types by dropping them into your Google Drive folder from elsewhere on your Mac. However, Google being Google, the company is also adding a few extra goodies for your files: support for optical character recognition (OCR) and location recognition. The former will scan your PDFs upon upload and yank out any recognizable text; you can then convert the PDF into an editable Google document. The latter—location recognition via Google Googles—attempts to add searchable tags to your images (for instance, if you take a photo of the Empire State Building, Google should theoretically label it "empire state building" for easy searching later). That said, the company describes location recognition as "still in its early stages," and rightly so—it's likely that Google will need to index quite a few Empire State Building pictures before it can identify yours.
Dropbox or Google?
For Mac users new to the concept of cloud storage, Google Drive may prove to be more popular in the long run. It has a built-in base of Gmail users, and Google Docs integration is pretty great for anyone who collaborates on documents and likes to be able to easily launch or sort those documents without working through a Web interface 100% of the time.
That said, I'm personally unconvinced as to Google Drive's superiority. Though Google's monthly space subscriptions are cheaper ($5/month for 100GB versus Dropbox's $20/month), we have yet to see Drive's stability in comparison to Dropbox's. (As with many of its new services, Google appears to be rolling Drive out gradually, presumably to manage the demand.) Upload and download speeds also seem drastically slower for Google Drive than for my Dropbox, at this point.
For many, though, it will come down to trust. While I don't necessarily think Google is going to do nefarious things with my data, the service operates like many of the company's other offerings, relying on your information to anonymously improve its services for other users—in this case, OCR and location recognition.