When you 'work under' someone you are employed by them or instructed by them. You can work under a manager, a supervisor, a professor or an organisation. This is another way of saying you 'work for' someone or a good expression to use if you want to make the hierarchy of your workplace clear. You might also say you 'work well under pressure', meaning you can perform well even in stressful conditions. You will hear this phrase mainly used in professional contexts.

1. I work under Mary, the head of my department.
2. Philip hated working under his new boss as he disagreed with his management style.
3. I can't handle working under so much pressure! I think I'm going to crack up!