This idiom means to organize your life or work in a better, more efficient way. It is essentially taking action to improve yourself. That can be achieved by setting yourself clear goals and creating a plan to reach them, or by correcting character flaws or general poor behaviour.
It is quite common for someone in authority, such as a parent, boss, or teacher, to command someone to 'get their act together.' It is usually said firmly, sometimes as a warning, but sometimes with the intention of forcefully encouraging that person to improve or succeed.
As the video shows, this expression is common in both a social and professional context, and is similar to the phrases 'get your house in order,' and 'cop yourself on.'