The storage indicator that you can see in the top bar (just below you user name) and on the settings page, warns you before reaching the storage limit. Once you go above that limit you won't be able to send more files. Note also that in this case other people can still use your "Receive files" page, but you won't be able to download received transfers. To get back on track you need to reduce the amount of stored data by removing some of your transfers: Read how to clean up your data.
Another alternative is to upgrade your account (if you are not already on the Enterprise plan). The top tier subscription allows to store up to 5TB of data. If you need more - just get in touch with us.