I would suggest that you
test sending of e-mail in a plain old Java application first, like a small command-line program which does just that and nothing else.
Tomcat and Servlets aren't really easy to use for basic testing.
And make sure that your setup agrees with the assumptions that I see from your post:
1. You are running an SMTP server on the same computer where the code is running.
2. It is listening at port 25 (which is the default port for SMTP).
3. It doesn't require authentication.
4. It is configured so that it can relay e-mails which claim to come from a different domain (gmail.com in your case).
You should also become conversant with the administrative functions of that SMTP server, so that you can tell whether it has delivered an e-mail successfully. Or if it isn't your server, you should enlist the help of its administrator.