But what if I'm doing my own project? For most of the time, I know how the parts of the system interact. All I need to do is to write a bunch of unit-tests. What are the possible situations when I would need Cucumber then?
You still need Cucumber. You need it to document how you see the system working, and you need it to make sure you haven't broken functionality when you change things.
In other words, you need Cucumber stories for the same reasons as you need unit tests -- they just work on a higher level of abstraction.
