To undertake something means to commit yourself to doing it, especially when it's challenging or requires serious effort. When you undertake a project, you're taking responsibility for getting it done and accepting the obligation to see it through.

The word carries a sense of deliberate commitment. A scientist might undertake a five-year research study. A construction company undertakes building a bridge. When you undertake training for a marathon or learning a musical instrument, you're making a real promise to yourself to see it through, even when it gets difficult.

Notice that people usually undertake things that matter and require sustained effort over time. You wouldn't say you undertook eating lunch, but you might undertake learning to cook. You wouldn't undertake walking to school, but you might undertake a 50-mile hike through the mountains.

The word suggests both intention and responsibility. When someone undertakes a task, they're accepting the obligation to follow through and take ownership from start to finish. If your teacher asks you to undertake organizing the class library, she's trusting you to take ownership of that job from start to finish.