What Is DHCP (Dynamic Host Configuration Protocol)
In simple terms, Dynamic Host Configuration Protocol (DHCP) determines if an IP is static or dynamic and the length of time an IP address is assigned.
Dynamic Host Configuration Protocol is controlled by a server. A router can be a Dynamic Host Configuration Protocol server, and on most home networks, serves this purpose.
This might be confusing because the word dynamic is in the term, but just because DHCP is enabled on a computer doesn't mean it can't be assigned a static IP. Having this feature enabled on a computer simply means it's letting a DHCP server assign its IP.
A true Dynamic Host Configuration Protocol server (not your Linksys router) gives the LAN Admin a ton of control with IP address assignment and IP address management (IPAM).
Ever print to a network printer? Ever wonder how that printer keeps its network assignment? Each network device has a MAC address. The LAN administrator 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. By printing the network configuration at the printer, it will determine whether or not DHCP is enabled and how the IP is assigned.
DHCP Via ISP
Your ISP has a Dynamic Host Configuration Protocol server. They can assign IPs by modem MAC addresses. When your modem comes online, it communicates to the network indicating it is looking for an IP address. The DHCP server listens to this communication and starts talking to the modem. The modem then transmits its MAC address to the server. At that point, either an IP has been reserved for the modem or one is assigned at that time. Hence cloning your MAC address to get a new IP from your ISP.
DHCP Via Router
Under the General Setup or LAN Setup tab in most routers, there is a setting option for DHCP. This option can control how many IPs are assigned or to enable/disable the server portion of the router. If this option is disabled, an IP address will have to be statically assigned to each computer, or have a DHCP server on the network. This goes for wired and wireless. Any connection on a network must have an IP address.
There's a lot more to Dynamic Host Configuration Protocol servers than this, but this is a basic explanation.