A dynamic DNS (domain name system) service is a company that charges a small fee to allow a user connecting to the Internet with a dynamic IP address to be able to use applications that require a static IP address.
Using a dynamic DNS service works as if there was an old-fashioned telephone message service at your computer's disposal. When a user registers with a DNS service and connects to the Internet with a dynamic IP address, the user's computer contacts the DNS service and lets them know what dynamic IP address it has been assigned from the pool; the service works with the DNS server to forward the correct address to the requesting computer. (Think of calling the message service and saying "Hi. I can be reached at 4188.8.131.52 right now. Please tell anyone who tries to reach me to call that number.) Using a dynamic DNS service to arrange for computers to find you even though you are using a dynamic IP address is the next-best thing to having a static IP.