ARP Spoofing is a method someone such as a hacker) could use to redirect traffic from a computer through the hacker's computer and then to the internet. This allows the hacker to then read all traffic sent from or to the first computer. This will reveal passwords, credit card numbers, and other private information.
A symptom of this sort of attack is a window when browsing to a secure site that says something along the lines of "This website's authentication check has failed". This means that the hacker has forged a secure connection that cannot be verified. So, the warning is presented.