Thanks to moonboots for pointing out my mistake. I forgot to fill the curve before converting it to a mesh. You can see the solution in the screenshot below:
I have created a (closed) bezier curve. After that I changed the mode from "Edit Mode" to "Object Mode". Finally, I selected the whole curve and hit "Alt+C" to convert it to a mesh.
However, all of a sudden now it does create a mesh but it seems to be empty. You can see the background grid through the mesh because there does not seem to be the default blueish grey color on it.
I have successfully used this method before to convert a curve into a mesh and I can't find what I have done wrong/ different now.
I have already used Google to find a solution but looking for the term "Empty mesh after mesh from curve" has not given me any results. And looking for tutorials for creating a mesh from a bezier always give me the same error.
There is also a screenshot attached. I can also upload the project file to Dropbox if wanted.
As you can see the selected object is a mesh since it has the triangle icon.
Thanks for any answers. I have already spent quite some time to find a solution but nothing helped me to solve the problem.