In simple terms, DHCP determines if your IP is static or dynamic and the length of time an IP address is assigned.
Dynamic Host Configuration Protocol is controlled by a DHCP server. Your router can be a DHCP server...and if you're on a home network, it most likely serves this purpose.
I know this might be confusing because the word dynamic is in the term, but just because you have DHCP enabled on your computer doesn't mean you can't be assigned a static IP. DHCP enabled on your computer simply means you're letting a DHCP server assign its IP. Having it enabled DOES NOT mean it's a DHCP server.
A true DHCP server (not your Linksys router) gives the LAN Admin a ton of control with IP assigning.
Ever print to a network printer? Ever wonder how that printer keeps its network assignment? Each network device has a MAC address. You can assign a static IP at the server to a specific MAC address. This allows the network printer to always get the same IP even after it reboots and without assigning the IP at the printer. If you print the network configuration at the printer, it will probably tell you that DHCP is enabled and no static IP is assigned. That's because the IP assignment is handled at the server.