Observing your thoughts while meditating refers to the idea of trying to remove yourself from your thoughts and see them from an external perspective. In this way, you may be able to let some of your thoughts go, especially if they are small details that will not have a large impact on your life in the long run.
If you are worried about what the grocery store clerk thought about your messy hair for example, by observing your thoughts you may be able to realize that this type of worry is not something that will impact your life in a meaningful way.