Address Resolution Protocol, or ARP, exists to create a mapping between an IP address to a MAC address. ARP's behavior differs whether you are communicating with a host on the local network, or a foreign network. This video explains traditional ARP in less than 5 minutes.
But there are additional iterations of ARP, such as Gratuitous ARP, Proxy ARP, and ARP Probes and Announcements. To learn the functionality of each, check out the ARP Article Series at Practical Networking .net: