Your lights please to a noob. I recently got my Atom along with DT 770 pro 250ohm. If I don't use gain, the volume I get is exactly the same as my onboard sound card and I have to crank it to 2-5 o'clock to be somewhat fine. With gain, it sounds really fine and loud around 12 o'clock and by 3 o'clock is already too loud, but I wonder if gain has an impact to the sound quality. I hope not because without gain I get no difference volume wise compared to my onboard solution.
I haven't checked all the pages so I dunno if there is a graph that compares low and high gain, but it's generally understood that for the Atom, you get no additional audible distortion at high gain. If you measured it however, it would probably be a bit higher on the graph for high than low gain, but again, this shouldn't be audible at all. The Atom is regarded to be one of the cleanest amps out there, in the same league as THX AAA 789.
The main purpose of the switch is that different headphones need different amounts of power to drive; on a sensitive headphone, the high gain would be way too strong and the volume knob would therefore be somewhat annoying to use as you'd only ever have it slightly turned up and it would already be too loud. So the gain switch lets you deal with that by giving you different settings for hard to drive vs easy to drive headphones.
I'm pretty sure the 250 Ohm DT 770s are difficult to drive; slightly easier than my 250 Ohm DT 990s which are the open-back version of the 770s, but still. These seem to be pretty difficult to power, my DX3 Pro just barely gets my 990s to a comfortable listening level at high gain, but with zero headroom for quiet tracks; I'm definitely going to need a better amp in future for them. =)
(FYI, the DX3 in high gain has about half the power as Atom in high gain, if you're curious for comparison purposes)