From what I understand, variance is a word coined to refer to the WAY in which the results of a particular game will vary - sometimes you win, sometimes you lose. But:
In a "high variance" game, you will typically get lots and lots of losing games, and then less commonly, some okay games, and infrequently, some really good wins, and the RAREST games render the HIGHEST returns, which are often VERY high - like these DoA 3500x bet, 4000x bet, 4927x bet, whatever it is.
In a "low variance" game, you get a fair amount of winning games, though the wins aren't so high, and the highest wins are maybe 200x your bet or lower.
But if we assume that both high and low variance games have a return to player of, say, 96%, then both games will - in theory - be equally profitable for the casino, as well as the player. But rare winners on high variance games will get huge wins, and winners on low variance games will get modest wins.
It sounds complicated, but as they say about even sending men to the moon, it's a complex concept built of lots of simple concepts.
Randomness is an even more complicated concept that I'm not sure I can explain well, and not even sure I understand it fully. From what I've read, it sort of means that for any game that you play, any other player could have gotten those exact same results if instead of yourself, THEY had ordered that game at the exact same millisecond you did. In other words, randomness does not discriminate on the basis of race, gender, sexual orientation, or the fact that you won a jackpot just last night - it doesn't discriminate, period.
I think I'll let others chime in, if they wish, but I hope this helped clear up some confusion, instead of creating more, lol.