A DHCP server is the one which provides a network client with a unique IP address, Subnet mask, Gateway and DNS server IP address automatically when it connects to the network.
A DHCP Relay Agent is a computer, server or a Router in a particular subnet which receives a DHCP client broadcast and relays it to a DHCP server in another network or a subnet. A DHCP Relay Agent is more a helper agent here that gets the client a DHCP lease.