There are few ways (not comprehensive) to prove that your application is encrypting information:

 1. [SSL Labs][1] has a web application to test your web application's SSL implementation
 2. In your web browser, sites secured with HTTPS will show a green lock next to the URL like so:
 [![a picture that shows the green lock icon next to the URL for][2]][2] 

If you need better proof than the green lock, click that lock, show details, and you'll see something like this (in Chrome for this example):
[![details that describe the certificate is encrypting your connection and working properly][3]][3]

 3. Fire up Wireshark, or a packet sniffer/analyzer of your choice, then run some data through your application that should be encrypted (login, submit a form etc...). Find the packet, follow the TCP stream, and check to ensure nothing is transmitted in plain-text.