I can not think of intuitive meaning of F measure than it's just combined metric.
What's more intuitive than F-mesure, of course, is precision and recall.
But using two values, we often can not determine if one algorithm is superior to another. For example, if one algorithm has higher precision but lower recall than other, how can you tell which algorithm is better?
If you have a specific goal in your mind like 'Precision is the king. I don't care much about recall', then there's no problem. Higher precision is better.
But if you don't have such strong goal, you will want a combined metric. That's F-measure. By using it, you will compare some of precision and some of recall.
ROC curve is often drawn than stating F-measure. You may find this article interesting as it contains explanation on several measures including ROC curve: http://binf.gmu.edu/mmasso/ROC101.pdf