First, draw a mental picture of the typical carrier network. There are a bunch of "black telephone" endpoints connected in various ways (but primarily by copper loops) to a central office, where there's a Class 5 switch and trunk connections out to the world. Where trunks interconnect with other trunks (particularly long-distance trunks), you can add to your mental picture fast but less-feature-laden Class 4 switches.
Now draw some next-gen IP technology into our mental diagram. As we move to a world in which some of the vast PSTN system is replaced with IP-based alternatives, we find that we have to pencil in some media gateways so that we can take a call made on traditional circuit and recast it in IP packets (and vice versa). Since the existing PSTN is at least smart enough to have a separate network for signaling (SS7 that is), you'll also need to sketch in gateways between SS7 and IP signaling (where the installed base is largely H.323, but the future seems almost exclusively aligned around SIP).
You're going to need some software to coordinate between signaling and the actual IP packet streams generated by the calls. In fact, you're going to need some pretty intelligent software, because you may need to make complex access and billing determinations about calls in real time, may need to execute complex series of "find me" routing decisions, and may in fact have to think pretty hard just to find the right gateway to redirect a call back to the PSTN so that it can be terminated on the right black phone back in the real world.
If you make this last addition to our mental diagram in the form of control software running on a conventional Unix box, then what you have just sketched in is a softswitch.
While the mental picture is fairly simple stuff, there are all sorts of roadmaps for how to go about translating the theory into products. Since softswitches are software, you can run them on boxes that look and act in every other way like a media gateway. Or you can tie the control of several gateways (using the MGCP protocol) to one softswitch running on a separate box, presumably at some physical remove from each of the gateway boxes. Some vendors think SS7 signaling translation may as well be handled by the softswitch, while other vendors sell separate SS7 gateway boxes.
In other words, what the "softswitch proper" does is clear, but the ecosystem surrounding it couples various parts and pieces in different ways. The ecosystem "is by definition amorphous," says Houman Modarres, CommWorks Corporation's director of softswitch and IP telephony product management. That flexibility leads to the hope and promise -- and simultaneously to the confusion.