No problem! Read on...
What is DNS:
The domain name you bought has to be mapped to an IP address. For example www.weebly.com is mapped to 188.8.131.52. When someone types in www.weebly.com, their computer looks up the corresponding IP address through their local DNS server.
The problems with dynamic IP:
If the IP address is dynamic, like many ISPs provide, then you would have to change the mapping every time the IP address changes. In addition, a local DNS server might cache the mapping for up to 24 hours, so even if you do change the mapping on your DNS server, the user's DNS server might not know.
Dynamic DNS services offer a service where they will look up your IP and change their records as soon as the IP changes. Also they will set the TTL (time to live) of the record to be small, so that well-behaving DNS servers will not keep in in cache for more than a few seconds. Problem solved!
Google for: Dynamic DNS.