There are several reasons why CF7 can't submit your data. The error is always shown in red letter.
01. Check if you have filled all the required field of the form.
02. Your CF7 settings in the backend is OK.
03. Your host is not blocking any outgoing mail delivery port. This happens mostly in shared hosting.
If everything is OK, but you are still getting an error message like the following:
Then check if your MX record are pointing to the current server. Hosting like namecheap shared will not allow msg to be sent from this server if the MX record are pointed to some other services like Google.
On this case you need to configure an SMTP plugin like: https://wordpress.org/plugins/wp-mail-smtp/
so you can send mail from your won mail server.
A free gmail account can be configured to do this mail routing. THese plugins have good documentation.
Let me know if you are facing problem like this.