Why would you want to measure stuff, other than for the sake of market research?
Counting is measuring. Why do you need numbers?
Math is measuring.
Speed limit is measuring.
Weight is measuring.
Height is measuring.
Distance is measuring.
Why would we want to do any of those things?
Money is basically a proxy to represent someones time. It is a universal exchange tool used for people to exchange tokens of time. Without money you might have a farm and need my help. You say "Hey, if you help me for a day on my farm and I'll give you 3 chickens". It is an exchange of my time (a day) for 3 chickens. Money simply provides a universal exchange tool for converting between all other forms of goods. I can exchange time for money, and use it to get whatever I can exchange for an amount of my time proxy. I could thus maybe buy 1 chicken, some bread, and some vegetables instead of simply having to settle for 3 chickens.
So money in a sense is a measure of a person's time. That's about it. :)
Yet we measure vast amounts of things. You certainly cannot do any form of engineering, or programming without it.
In programming we measure things in bits.
Without measurements we end up basically with one, a couple, a few, some, a lot, etc. It becomes very ambiguous and subjective.