Static IP addresses remain fixed, that is to say unchanging. Static IP's are advantageous if you are interested in configuring your device with a DNS server, also in the case of setting up a host server (VPN, Webhosting, Email, etc.), and for the reliability and direct access that an unchanging IP address provides. Some pitfalls to keep in mind is that an unchanging IP is generally higher cost and higher risk than a changing one - static IP's can be thought of as 'sitting ducks', or unmoving targets. Therefore sufficient understanding of the security concerns surrounding static IP's should be gathered in advance.
Dynamic IP addresses are dynamically assigned by Dynamic Host Configuration Protocol (DHCP), and may be changed at any time. Dynamic IP's are advantageous for general users as they self-regulate, and are lower cost with less security concerns at play. They are less reliable than static IP's, but depending on the intended use of the device it may not make a discernible difference.