In Breaking-Bad Walter White leaves Gray Matter and becomes a chemistry teacher. What compelled him to take up a second job? Is there any significance of his second job?
Walt took the second job to add another source of income for his family. Do not forget that Skyler was pregnant at that time, and that meant Walt's family was going to expand. Obviously, Walt did not make much, through his primary job of a High school teacher. So with a wife, disabled son and an upcoming baby, and Walt being the sole bread winner, his choice of going for a 2nd job is obvious.
Also, do note that Walt is not treated nicely at his 2nd job, but he still carries on, for reasons most people do jobs in the world - to provide for their family.
According to Brian Cranston, the key driver for him taking a second job was that he was short of money due to his family situation.
"That's Walter White. That's the hook or the bait for the audience: Walt's humanity, his humiliation as he was scrubbing cars at the car wash, trying to make extra money for his special-needs son; or his passion in the classroom, his desperation to see an interested pair of eyes.
He has very, very low hope, and his own missed opportunities, and cancer. He's gonna die. He doesn't have money. He has an intellect and so it became a perfect storm. He knew how to make meth. He was introduced to it because of his brother-in-law. The stacks of money, the pressure, dying, his family taken care of the rest of his life. Gah! Snapped!
"It set the table for everything that the series was going to show you. ... That moment in the classroom, where he gets lost in the joy of chemistry, and he's trying to share his joy with the class. He looks out and he sees this sea of apathetic faces of his students. And he just gets so depressed that he wonders, Have I wasted my time? What am I doing with my life? No one cares. No one gives a shit about science. ... The next thing, he's at the car wash because he needs extra money to pay for his son's physical therapy, and [he’s] chided and ridiculed by his students. This man is just down at the bottom. And then he finds out he's got terminal lung cancer."