I was wondering why that thread was in the bucket... got confused for a second...
a power struggle occurs when you and anothe person shoot a beam at eachother and they collide. this lets you enter a power struggle in an attempt to defeat them(like during the Saiyan saga when vegeta shot down at the earth and goku shot a kamehameha back at him)
anyways to elaborate on the blue and red bar, like fatmanterror said it shows your status in a power struggle. when the line is in the red, you are losing, but when it is in the blue, you are winning. holding down the attack button(left click by default) you pump ki into the struggle which helps you win. If you push T to go turbo, you get even more strength to help you win. You just have to watch how much ki you have, if you run out, then you are done for.