the software synchronises SMS from your device to the cloud so you can access it from the browser. You will see all your messages in both browser or app. Messages between mysms users are free.
I have this installed on an Android device for testing a few weeks ago and it looked like a good idea.
Just tried installing it on my Windows Phone and it says my phone number is in an invalid format. I have one of the six digits Vodafone numbers (+64 21361xxx) and I suspect the app is expecting a minimum length of seven or more. Reported this here and if you have the same problem please let them know by posting in that thread.