To brush off literally means to remove something ( dirt/dust/foreign particle) from someone through the act of brushing or using a brush. eg. To brush off an insect from one's shirt. To brush off something/someone can also mean to not take something/someone seriously or to belittle it's/their significance. Eg. Frank brushed aside the tantrums of his daughter as a normal sign of teenage.

brushed off = not taken seriously

A few ways to describe it as an expression would be..... To brush something off can mean you don't wan't to do something so you keep making up excuses not to do it yet, or keep telling yourself that you will do it at another day/time(prolonging doing something) Example : You need to cut your grass in the yard(mow your lawn), but you really don't feel like doing it. So everyday you keep making up excuses why you can't cut your grass(mow your lawn). So you might tell yourself, I can't cut the grass today, because I have to go to the stores, etc... so I'll do it tomorrow. Tomorrow comes around, and you tell yourself again, I can't do it today, because I want to go see Jessica today. I'll cut my grass tomorrow, etc... until you finally decide that you're ready to do it/have to get it done. haha Example of brushing someone off : A girl keeps calling you, asking when are you going to come see her. But you think the girl is annoying, so you keep "brushing her off". You keep making up excuses(lying to her, in this instance) everytime you talk to her. So you say " Oh sweetie, I can't come see you today because my mother's car broke down and I have to go pick her up from somewhere far. So a few days later the girl calls you and you say "Oh baby, I was definitely planning on coming to see you today, but I have to freaking work late tonight because my boss is a jerk!" So finally one you are bored and she calls you and asks if you're ever going to have time to come see her. So you say " Of course honey, I was supposed to go visit my father today, but I told him it will have to wait, because I haven't got to see you in a while, and I miss you"... So you finally go see her after brushing her off for over a week or so. But all these were lies and I wouldn't recommend anyone to lie. I just made up this little storyline to try to help you better understand the meaning of the expression in certain circumstances. It's always best to be honest, especially with women. It's always best to just be truthful with others. I hope this helps you get a better understanding of just a few of the meanings of the expression. Good luck :)