In the simplest terms:
- if you install free Moodle on your desktop you can't easily run courses for students on it because it is just on your desktop and not on the internet. (Some people will try to tell you that you can, but it's very complex) People do this to test Moodle.
- MoodleCloud is a service offered by the people who make Moodle and they (we) set up a Moodle site online for you so you don't have to do the technical stuff and can just get on with teaching your class.
There are longer answers and more details but hopefully that helps. Also - I see you are currently in our Learn Moodle MOOC. You could get yourself a MoodleCloud site to try restoring your practice course, if you wanted to.