Each time a visitor submits a Contact Form to you, you will get a notification of what was submitted and how many form submissions you have left. You can upgrade your plan at anytime, or you can delete existing submissions or file uploads to make more space from your client area.
If you do run out of form submissions or file space you will continue to receive email notifications of new submissions but they will not be added to your contact form management section in your client area.
If you run out of file space, you won't be able to receive file uploads from visitors and your visitors will get a warning that the file can't be uploaded if they try and send you a form submission with a file upload.