Score in itself, is the sum of an empire's current non-millitary accomplishments. While the number doesn't mean much in itself, by looking at the other charts you can find out quite a lot about that civilization by its relative score. For example, (a generalization that has always held true for me but could be incorrect) any civ under 900 pts by 1000 AD playing monarch-immortal has been heavily beat on, and really is no threat for a long time, due to lack of cities, and quite possibly is someones vassal.
If an Ai is low in tech, yet running away in score, chances are they have conquered much of the land around them, and have several stacks of doom waiting for the unwary.
A far more accurate chart to look at before going to war is the power chart. On high difficulties emporer and above it will be scewed by your relatively low population, but still a power graph 2-3 times greater than your own will spell almost certain defeat in a fullscale war.