How IP helper address works and what is the difference between dhcp and IP helper-address .please explain in brief.
ip helper-address command sets up a DHCP relay. DHCP only works on the LAN to which it is connected because it uses broadcast, which cannot cross a router. To remedy that situation, DHCP relay was created. It gives DHCP an option so that a router intercepts the DHCP client's broadcast request, creates a unicast request to the DHCP server on a different LAN, and the DHCP server can give a unicast response to the router based on the DHCP option, that then passes on the DHCP response to the requesting DHCP client.
To add to Ron's great answer:
The key piece of this is that the Router sending the DHCP request on behalf of the client will unicast the request with a source address from the address space the client is in (the interface the relay/helper-address is configured on). This is ensures the DHCP server offers an IP from the correct scope.