Without spoiling anything can anyone answer my question?

What does it mean if I tell Yes Man to ignore a faction like the Brotherhood of Steel or the Great Khans? I'm a little confused on this and don't want to screw something up.

It basically means, you are good with that faction. You pretty much have two choices. Either destroy the faction or "ignore" it. By saying ignore, you are saying to yes man "ok they are good, lets go to the next faction."
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I thought by ignoring you just didn't want to deal with them. I kept waiting for a "they're cool, let em be" kind of thing.

Well, by ignoring a faction, you're basically saying for Yes Man to let 'em be. The only other option is to waste the hell out of the faction with bullets/lasers/plasma/explosives and tell Yes Man that the faction "won't be a problem" anymore.

Oh. I was under the assumption I could "waste" a faction, "ignore" a faction, and "side" with a faction. Sided factions be my cool Vegas buddies. I guess I was horribly, horribly wrong.

Independent Vegas is just that - independent. You don't run the whole world, you merely run Vegas. Everyone else is content to ignore you and go about their business, or develop a trading relationship with you. If you were meant to rule the Mojave, the quest wouldn't be "No Gods, No Masters", it would be "I'm God, I'm the Master" since you're technically ruling then.

I do enjoy Yes Man's response when you say to ignore the Brotherhood.

This.