It defines the number of router hops the packet is allowed to make before it gets discarded. At each hop the counter gets lowered by one until the final router notes that the counts are all gone and discards the packet. The mecanism is there to prevent packets rattling aroung the routing infrastructure/internet forever when for some reason (such as a routing loop for example) they don't get delivered to a destination.
My Server 2003 book also says that the TTL will decrease by 1 if the packet takes longer than 1 second to reach it's next router. Is this true? I've never heard of that but I suppose it would make sense.