The private IP addresses of individual devices can change though, depending on the configuration of the DHCP server.
To be able to reach Raspberry Pi on the same address in your own LAN, you have to provide it with a static, private IP address.
Find the DDNS support tutorial for whichever individual router your DDNS server is intended to operate on, such as this tutorial for Linksys routers.
Many routers support the ability to provide individual devices within the local network with a static IP address.
One such static IP address for Raspberry Pi can be used, for example, for the remote maintenance of a computer within the network protocol SSH (Secure Shell): If you have an SSH program installed, you can control the Raspberry Pi via another computer using the SSH client.