Let me be clear, I should have checked my head-fi subs a little earlier to spare you from any confusion, sorry about that!
An LOD generates a sound signal which is audible, but is at a fixed low volume to spare you from the horrendous crap of an internal amp, now I don't believe it COMPLETELY bypasses it (hence the existence of the iMod) but it's much better.. You need to boost that signal either by plugging that into the input of either a receiver, powered speakers (ones that are plugged into a wall or battery operated) or a headphone amp. It will not put out any volume that is useable for headphones.
Ipod > LOD > amp > cans > head
Ipod > LOD > receiver> cans > head
Ipod > LOD > speakers
Ipod > LOD > speakers > headphone jack to cans > head
All of those work and should sound better than what just the headphone output!
For example my choir teacher in high school used to notice that the headphone out sounded like poo so he connected his ipod dock to the receiver over speakers instead of just a simple 3.5mm from the headphone jack to RCA's and it sounded much better that day!
This was before I was in head-fi so I just thought it was magic or something.
A DAC takes a digital signal, which is more or less just raw data before it's even become sound, think of it like you actively transferring the song file into a little machine that cranks out actual unamped audio signals, the signals then need to be amplified, either by an internal circuit or an amp to produce audible sound. Most DAC's have an amp, a lot don't. This bypasses your internal soundcard of whatever the USB/optical is plugged into.
computer/ipad > DAC > amp/internal amp > cans > head
Hope this clears stuff up!