DHCP, or Dynamic Host Configuration Protocol, is the protocol used to dynamically assigning IP addresses to remote clients. It's used on many local networks, and used almost exclusively by ISPs when assigning IP addresses to computers connecting to the Internet.

The process of assigning the IP addresses by the DHCP server known as DORA (Discover, Offer, Request, and Acknowledgement).

APIPA stands Auto Private IP Addressing takes effect on Windows 2000 Professional computers if no DHCP server can be contacted. APIPA assigns the computer an IP address within the range of 169.254.0.0 through 169.254.255.254 with a subnet mask of 255.255.0.0.

A switch,  keeps a record of the MAC addresses of all the devices connected to it. With this information, a switch can identify which system is sitting on which port. So when a frame is received, it knows exactly which port to send it to, which significantly increases network response times. And, unlike a Hub, a 10/100Mbps switch will allocate a full 10/100Mbps to each of its ports. So regardless of the number of PCs transmitting, users will always have access to the maximum amount of bandwidth. It's for these reasons why a switch is considered to be a much better choice then a hub.
Routers are completely different creatures. Where a hub or switch is concerned with transmitting frames, a router's job, as its name implies, is to route packets to other networks until that packet ultimately reaches its
destination. One of the key features of a packet is that it not only contains data, but the destination address of
where it's going.
A router is typically connected to at least two networks, commonly two LANs or WANs or a LAN and its ISP's network (ex. your pc or workgroup and EarthLink). Routers are located at gateways, the places where two or more networks connect. Using headers and forwarding tables, routers determine the best path for forwarding the packets. Routers use protocols such as ICMP to communicate with each other and configure the best route between any two hosts.
A router will typically include a 4-to-8 port Ethernet switch (or hub) and a Network Address Translator (NAT). In addition, they usually include a Dynamic Host Configuration Protocol (DHCP) server, Domain Name Service (DNS) proxy server and a hardware firewall to protect the Local Area Network (LAN) from malicious intrusion from the Internet.

DHCP is a Dynamic Host Configuration Protocol and it will allocate IP address to clients during startup.
DHCP is typically used for reservation and allocation of IP address and it reduces the Human errros.