Your application has two important purposes: It should clearly identify the goals of your project, and it should convince us that you are the right person for this task.
In particular, your application is your opportunity to show us that you understand what you'll be doing for the task, and to demonstrate that you've spent some time thinking about it, its difficulties, strategies for overcoming these, and have a good estimate of how much time they will take.
We don't expect you to produce a perfect application without any help at all. We strongly encourage you to discuss your application with us while you're preparing it, to ensure your ideas align well with our own thoughts on the tasks. It is also the perfect chance to already get to know your potential mentor and the rest of the team.