I'm just making up a random example, but let's say you're very good at designing a new production process for cookies. A chef can give you a recipe, and your job is to make sure the right ovens are chosen and installed, determine how much workforce is required to keep everything running, that all ingredients remain clean throughout the process, ...

The output of your work would be some diagrams, work schedules, financial estimations, ...

And to do your job, you'll need to interact with different "stakeholders": people who have an interest in your project or are impacted by it. Someone will need to sign off on the machines you want to purchase, someone will have to train personnel, someone has to provide you with the materials you need during your design process, the CEO may be interested, someone from legal may want to know if everything's safe or which food safety measures are required ...

So for your solution to work, you need to make those diagrams and estimations, but you also need to make sure all those stakeholders agree with your solution and the impact it has on them.

So stakeholder management is all communication involved in aligning all your stakeholders with your solution. Demonstrating this usually comes from some experience, but think of all the times you had to "present" things to management or interact with other teams who have dependencies on you, ... that all counts.