DHCP, or, Dynamic Host Control Protocol is a standard that allows one central source, i.e. a server or router, to automatically assign requesting hosts an IP address.
The most common DHCP servers on Linux platforms are the ISC’s (Internet System Consortium) dhcpd, and dnsmasq. On Windows platforms there are a variety of DHCP servers, though the Microsoft DHCP server is arguably the best in terms of support and integration.
dhcpd is the most common DHCP server, and it offers excellent integration with BIND (DNS server).
DHCP helpers are sometimes referred to as DHCP relayers. The basic idea is that a relay agent will forward DHCP requests to the appropriate server. This is necessary because a host that comes online on a subnet with no DHCP server has no way of finding the correct server; it needs a DHCP assigned address to find a route to the correct DHCP server, but can’t get there because it has no IP address! DHCP relaying solves this chicken and egg problem by acting as an intermediary. See this wikipedia  article for more details.