Basically a traditional radio would multiply a signal with the frequency you want to tune to and give you the resulting signal which is an audio signal. With an SDR, you can record the actual RF signal and then store/multiply whatever you want to. So you can store everything and later tune to any frequency using software later!

Basically what SDR lets you do (More properly the Quadrature Sampling Detector techniques they use) is record a large amount of radio bandwidth at once. So in this case I could record from 80Mhz to 136MHz. I'd have to then tune in to each frequency on the recorded data, but I'd have the entire spectrum there recorded to play it back later.

It's like recording a bunch of TV channels all at once, and then being able to go back and look at every channel at any given time in the recording.

The bigger issue with this particular device is that almost any antenna you use is not going to perform very well over such a large bandwidth, but that's a much nicer problem to have.

Yea, but if you record the whole spectrum then you can tune frequencies on the recording.

It's a bit like a color photo vs black and white. I don't know if that's a great analogy though.