To go down on a woman is to start her off with nice, long, passionate kisses on the lips, and then down to her neck, and then down to her breasts where you have your pleasure with them, and then you kiss your way across her tummy, and finally, you have ultimate pleasure with orally pleasing her pussy.
Almost the same for a man or a woman. But, to "go down on" a guy is right to the point. You don't start with his lips...It's immediately penis in throat.