To shirk your responsibilities is to avoid dealing with them — like when you watch four consecutive hours of infomercials instead of facing your homework.
A verb is an action word, so it's ironic that the verb shirk suggests inaction in the avoidance of work. To shirk carries with it a negative connotation of laziness. When Eleanor Roosevelt was asked how she conquered her shyness to become a powerful public figure, she responded, "I faced each problem as it came along. . . . I never tried to shirk. I tried never to evade an issue. When I found I had something to do — I just did it." Ah, Eleanor, why can't we all be a bit more like you?