Hi - Usually when people talk about starting out with a hot signal, they are referring to the level it hits the A/D converters at, or the level it hits the tape at. Either case is all about maximizing signal to noise ratio. In the case of digital, it's also about having better bit resolution, or more bits to describe the sound. With tape, it's also about printing the tape hard to take advantage of tape saturation, a pleasing sort of compression and coloration.
Assuming we're talking digital recording, the goal is to have the signal entering the soundcard or converters peaking at just at or below 0db, and not going over. With a soundcard, this is usually done by bringing up a software control panel or mixer applet for the soundcard, and watching the virtual meters on it while adjusting the output level of the preamp or other source feeding it. Most pre's also have an input gain that sould be adjusted first to give the desired sound, either clean and transparent, or driven and colored. Same goes with most guitar processors. Always adjust the input level first to get the desired sound, then the output level to set the record level to the converters.
Hope that helps, RD