What does this mean?

To “define,” at its most broad, means the designer considers what it is exactly they are trying to resolve. And then, the designer should be able to articulate (define) that problem.

Importantly, in this step, the context and insight gained from “empathizing” crucially influences that articulation.

In writing, this has the potential to be interpreted as generating a statement of purpose, or perhaps even most traditionally, writing the thesis statement. But where “define” differs from arguing a thesis is that the design-thinking process itself revolves almost entirely around audience and context. As both of those involve ever-changing people, new information not only complicates the writing & learning process, but it enriches the writer-learner’s connectivity and relevance to real situations. Because the definition of any problem very well could evolve, it’s important to remember that a return to an empathetic mindset is necessary.

Stanford's uses language like, "point of view" which aims to establish how you, designer, are using your new perspective to intervene. Here's a clip from the design thinking bootleg:

Writing studies scholar Scott Wible offers an example that helps concretize what it means to hone in on defining a problem. Allow this reconceptualization of “thesis” to underscore the purpose of the define phase: “Too often in the first weeks of [writing projects], in fact, students didn’t even engage in deep analysis or precise definition of the problem. Instead, they jumped right to proposing a solution. This type of proposal locks students into a limited understanding of the problem they are trying to address and, in turn, narrows their ideas about how to solve it.” [1]Wible, “Using Design Thinking to Teach Creative Problem Solving in Writing Courses.” pp. 403. By slowing down, and encouraging students to think as opposed to constantly produce, we can shape more intentional—arguably, better—writing.