The Basho blog has a couple of very good posts on vector clocks:
The problem statement was as follows:
Alice, Ben, Cathy, and Dave are planning to meet next week for dinner. The planning starts with Alice suggesting they meet on Wednesday. Later, Dave discuss alternatives with Cathy, and they decide on Thursday instead. Dave also exchanges email with Ben, and they decide on Tuesday. When Alice pings everyone again to find out whether they still agree with her Wednesday suggestion, she gets mixed messages: Cathy claims to have settled on Thursday with Dave, and Ben claims to have settled on Tuesday with Dave. Dave can’t be reached, and so no one is able to determine the order in which these communications happened, and so none of Alice, Ben, and Cathy know whether Tuesday or Thursday is the correct choice.
Vector clocks are used to keep the order of communications clear. Something you will need in distributed systems, including those for topic maps.