Converters just convert analog signal to digital and back again. Most instruments produce analog signals, such as a microphone, guitar, keyboard (although I suppose some of these also produce digital ones, and some start digital and output analog). A converter will take this analog signal and convert it into digital, so it can be sent to the computer (either via firewire, usb, or a few other options that are a bit more "professional"). The computer only works in digital, so in order to play back a signal, it also has to convert the signal back from digital to analog, since speakers work off analog signals. If you're unsure of what the difference between an analog and digital signal are, look it up. In short, analog is letting the flow of electricity represent the signal, where as digital is letting 1s and 0s represent the signal.
Most recording interfaces are actually multiple units in one. Most of them contain a few pre-amps, which will boost a weak signal such as a guitar or microphone to line level, which is what the converter expects to get to convert it to a signal. The converter than passes it off to the interface, whether it's usb, firewire, or something else, and sends the signal to the computer.
You could actually buy separate units to do all of these things, running a microphone into a pre-amp, which then goes out into a converter, which then pipes digitally into an interface such as
a Presonus V-Fire. There's actually all sorts of ways you can arrange things. For example, I have a an ART pre-amp with a digital output, which means there's a built-in converter on the pre-amp, so I can send digital signal directly to my interface without using the converters in the interface.
Anyways, I hope that didn't overwhelm you. It took me quite some time to figure a lot of this stuff out, but if you have any more questions or need any more clarification, don't hesitate to ask, you've come to the right place! We've all had to learn this stuff one way or another, and I think amongst a community of people who are just as passionate about it as you are is a great place to do it!