As your website grows it can easily run out of disk space (this can happen even if you don't update it, because you receive email and we collect statistics and reports for you that are all housed in your home directory).
When you run out of space there are a couple of things you should check, and the best way to check this is through the "Disk Space Usage Viewer" in cPanel.
A few things to look out for:
Check there are only files you want/need in your public_html, old files left behind in here can quickly mount up. High resolution images always take a lot of space, consider shrinking these for use on your website as not only will it save space they will be quicker to download for your website viewers.
Look for error logs (error_log) from software you've installed that isn't behaving as it should, these can be removed if they aren't currently generating errors but if they are you might want to look into the reasons behind the errors.
Check you've cleared your trash and spam boxes in your email (webmail or IMAP/POP3). We try to filter a reasonable amount of junk but there's always some left behind!
Check your default address is set to fail, otherwise your root address (<cpanelusername>@<yourdomain.com>) may have a lot of unaddressed mail building up in it.
Consider switching from IMAP where all your email account is stored on the server, to POP3 where you download it your local machine. If you need to keep recent mail online whilst out and about consider using both systems side by side.
If all of the above are clear take a look at the tmp directory, this is where the stats reports are housed for your domain and if you don't use them you can remove some of them (we'll start to create new ones again afterwards), more details on what you can remove are here.