Ping stands for Packet INternet Groper, and is a utility that is used to verify a connection to another connection on the network, remote network, Internet, ...etc.  It sends out a packet and waits for a response from the target.  Pinging is primarily used to test and debug network connectivity.
The Systems Department at CU*Answers might ask you to "ping" a few IP addresses to make sure you are able to communicate with devices before troubleshooting more complicated issues.