Measuring intracellular and extracellular water gives you a more complete picture of somebody's hydration status. Total Body Water does not give you any indication of whether you have a healthy ratio of intra to extracellular water, for optimal health this ratio should be approximately two thirds intracellular and one third extracellular. 

You may have a healthy amount of water in your body, however, if you suffer from water retention, this would only be highlighted when the ratio of intra to extracellular water was being monitored.  There are also many clinical applications to breaking water down in this way (Michelle would be able to cover these in more detail than me). 

From a sports performance monitoring aspect, any reduction in intracellular water can lead to reduced mental and physical function, so the ability to monitor this for individual players and therefore plan individual hydration strategies is crucial.