The Address Resolution Protocol handles the association between IP addresses and "hardware" (in XRPi's case Ethernet or AX25) addresses.
In order for IP datagrams to be handled by AX25 or Ethernet links, they must first be "wrapped" in AX25 or Ethernet packets. The destination addresses of these packets is determined by the process of "Address Resolution".
For example, imagine that you want to send an IP datagram to one of your neighbour nodes via RF. TNC's don't understand IP, so you can't simply transmit a raw IP datagram onto the airwaves. Your node must first "wrap" the datagram inside an AX25 frame addressed to the neighbour node. Upon receipt by the neighbour, the frame is "unwrapped", and the IP datagram it contains is handled by the IP router. Exactly the same process is required to send IP over Ethernet, except that Ethernet frames are used instead.
The destination address is usually obtained from an "ARP Table", that stores each neighbour's IP addresses along with their AX25 or Ethernet address. This table can be built manually using ARP commands, or dynamically. A typical ARP table would contain entries similar to this:
IP Address Type Hardware addr
------------------------------------------
44.131.91.2 AX25 G8PZT
44.131.90.6 AX25 G8JVM-5
192.168.0.23 Ether 00:12:34:66:21:DA
If the destination address is not in the ARP table, XRPi broadcasts an "ARP request" packet, asking if anyone knows the hardware address associated with the destination IP address. The destination node replies with an "ARP reply", giving the AX25 address that the datagram should be addressed to. XRPi adds this data to the ARP table, then uses it to wrap and send the datagram.
The "ARP entries" in the table usally have a finite lifetime (usually 15 minutes), because neighbours sometimes change their hardware addresses. This lifetime may be altered by the sysop.
When an entry gets too old it is purged from the table, forcing XRPi to send another ARP request, thus picking up the new hardware address. The sysop may override this by locking-in ARP entries.
A node other than the destination may reply, if it is the gateway to a "hidden" network containing the destination. This is called "proxy ARP" and is detailed in RFC1027.
The ARP protocol is detailed in RFC826.