As leaders we are expected to be able to make "off the cuff" remarks. Each of us needs to have a few pocket speeches and be ready to provide relevant context to the current conversation or situation.
Comfortable or not in these situations, it is important to know how to keep your extemporaneous comments short and finish strong. There is always a moment to stop talking and certainly a point at which you've gone on too long. When I consult with leaders about video I suggest having a strong, repeatable outro which includes a call to a higher purpose. The same holds for extemporaneous remarks. If you start to drift at all, hit your outro and be done.