ARP attacks use the Address Resolution Protocol to corrupts the IP to MAC address mapping on a machine in the local network. The ARP protocol is completely stateless and implements no security mechanisms. It is thus very easy to mascarade as another machine on the local network.
A successfull ARP attack be be used to eavesdrop, alter, inject or drop network traffic. A typical ARP attack example is a Man-in-the-Middle-Attack: Every network traffic that is exchanged between two machines on the local network traverses the attackers machine. Thus it is very easy to eavesdrop that traffic, inject or drop network packets.
A very good introduction to ARP spoofing attacks has been written by Sean Whalen: An Introduction to ARP spoofing. The corresponding slides are available here.
The first article about ARP spoofing attacks, called ARP and ICMP redirection games, was written by Yuri Volobuev.
More information on ARP attacks is available in the following documents: