As shown above, you can see your total capacity and space used, broken down into downloads and offline files, with the remainder being your available space. That gives you a pretty good idea as to what's taken up by the system and apps, and what you've downloaded personally. If you then need further info, you can check the files app (or abstruse chrome://quota-internals command).

Google Play has only arrived on a few Chrome OS models, including the ASUS Chromebook Flip (above), but when it's released in force, folks will get Android tablet apps numbering in the tens of thousands. Since those will take up space and generate their own files, storage info will become critical. If you want to test it yourself, you can download the latest dev update, then enable a flag.