Traditionally you need your computer to get PodCast: You use iTunes software on your computer to subscribe the PodCast, then iTunes downloads the PodCast periodically, and you use iTunes to synchronize with your iPhone or iPod, then you can take the PodCast on the go.
The innovation of Stitcher is that it leverages any available network connection (WiFi, Edge, 3G…) to directly push the PodCast to your iPhone/iPod Touch. So you do not need a computer and iTunes software to get the latest PodCast. You only need an network connection and the device.
I like this kind of innovation, considering WiFi access is becoming more and more popular and omnipresent.