Just adding a little more information to what Bruce and Regebro had to say: they're dead on, of course.
The other thing is the concept of "gain structure", which supplies the "why" for the things the other posters have said. This basically means that you want your signal to experience all the gain that it is ever going to need right in the mic preamp, before anything else ever touches it. Let's say that your mic level signal needs 60dB of gain to give you a 0dB (reference) level at the mixer's output. The mic preamp is designed and optimized to give you lots of gain with minimum noise. So if you set the trim for 60dB of gain, you can set the channel fader and master fader at 0dB (unity gain), and your levels are set. Happy, happy.
On the other hand, you could set the trim for 40dB, and then run the channel fader up against the stops at roughly +10, and the master at roughly +10 as well(the levels don't add linearly, of course, but bear with me for this example: the numbers aren't that important). It may seem like this achieves the same result, but think about it: the mic preamp produces some noise level. The channel fader makeup amp that amplifies the whole signal, *including* that noise, by +10dB. The master fader makeup amp then multiplies the (preamp noise*10dB) by another 10dB! Any way you slice it, this results in more noise than you need.
Bottom line is that you want to set the trims so that you get all the gain you're ever going to need right at the mic preamp, and not at the channel fader or summing buss makeup amps. They are good, but not as good as the preamp. If you get into the habit of setting levels with the trims, and then riding the gains with the faders (and EQs, and outboard gear) from unity (0dB) *down* whenever possible, you'll minimize the noise, and make the best of your gear.
Most people never really think about how noise stacks up: but adding more gain to an already noisy signal is by definition a hands-down lose.
