Generally the input levels are different because of the physical characteristics of whatever's generating the input.

Dynamic mics, e.g. most stage mics like the SM58 and SM57 produce a small signal and need the input gain turning up relatively high.

Condenser mics have higher output. In short, the reason for this is that they have some simple amplification built in.

Electronic devices that run on batteries or AC tend to put out much higher levels (called "line level"). Ipods, CD players and electronic keyboards come into this category.

The input gain control, usually a small rotary knob right at the top of the mixer's channel strip near the connectors, and sometimes called "trim control" or "gain trim", is the proper place to adjust the inputs to compensate for these differences. As Ray says, there may also be a "pad" button which introduces a big step reduction in the gain, basically to give the input control more range, and a "line input" jack which similarly has fixed lower gain than the mic input (to the same channel)

Joe asked what's PFL - that stands for Pre Fade Listen and it's a push button for each channel. When you press it that channel's signal after the input gain stage but before the main fader is fed to the headphone socket and a meter. You use it to set the input level so the meters kick but don't go too high on each channel, all about the same amount, and then everything should be reasonably well matched and you only need to use the main faders for fine adjustments of balance and they should all be set in the top half of their travel.

That leaves a puzzle for me:
The radio mic has a powered receiver that should pout out a hefty signal. So should the fiddle mic when used with its preamp. I don't know why they should need full gain on the mixer. It looks like something may be wrong.

Anahata