measuring is the process or the result of determining the ratio of  hysical quantity, such as a length,time and temperature. while counting is trying to figure out the number of things, or how much things cost.

Measuring is more important than counting becasue it gives you an accurate measure or balance of things. e.g it is important to measure how many tiles you would need for your kichen floor, than to try and count how many tiles are needed.

for deeper discussions go to Katie Paine's Measure What Matters Book.