SSB is a type of signal. It happens that boating people say "SSB" when they really mean "marine band HF", because SSB is the type of signal that you use on the marine bands. Amateur radio ("ham radio") also uses SSB on HF.
In the US, you don't need a license to use that radio to listen. Quite a lot of amateur HF equipment can receive all across the shortwave frequencies, so it is likely that you can use your radio to receive weather fax, other marine HF channels, regular shortwave broadcast stations, HF aircraft bands, etc etc.
Get the manual for the radio and see if you can get it to tune to a weather fax frequency. The audio sounds rather distinctive. (You can find sound samples on some web sites, or just know that it is a tone that varies pitch as it scans the dots on the page. There is a distinctive half-second period to it.)
I have used the Windows program at
http://www.jvcomm.de - it is a free demo download, and if you want to keep it, you pay for a key that turns of the "demo feature". (Specifically, it stamps DEMO DEMO DEMO over parts of the received image. You can try it and see if it works with your computer and radio; if it doesn't you lose nothing. If it does, you pay for it and get a fully functional program.)
I was happy with JVCOMM when I was using it. It made remarkably good pictures, considering the radio setup I was using. (I had a regular AM shortwave receiver with BFO, which you can fiddle with to make it receive SSB though it doesn't do it particularly well.)