The main thing that's great about measurement is it's easy to be objective. It deals with facts that we can quantify with numbers. Often we have measuring tools to aid us, e.g. timers, rulers, microscopes, etc.
We measure some things without tools. If I'm loading boxes onto a truck, I can count them one by one as I load them, and I can write down the count at the end (or even update the written count after every box). We count this as a measurement. Similarly, "I read book X" is close enough to the concept of measurement, and easy enough to evaluate, that one can think of it as a measurement or as similar enough. (Note the issue isn't whether you understood the book or paid much attention or gave it much thought. What's easy to judge or measure is whether you went through it page by page and read what it said. There are borderline cases like how many pages can you skip before it doesn't count? But let's not worry about that now.)
Something that's easy to judge, and involves physical objects and facts, is identifying objects or their traits. Is that a cat, yes or no? I look at it and say yes. Is that an apple? I look at it and say no it's a strawberry. Is that object red? I look at it and say yes (I could also measure that using a digital camera, a computer, and some software – and actually we now have software that's pretty good at classifying pictures as various objects like cats or apples). Is it a type of "measurement" to say that object A in my room is a chair and object B is a chair? That's just terminology. It's not especially important what we call it. Regardless, that kind of thing can easily be judged and used in our goals. We're good at doing that without being biased. It's the kind of thing we find hard to get wrong or lie to ourselves about.
What are some things we can't "measure"? Judging whether an action is moral, pious, honest, wise or fair. Saying whether raspberries taste good to me. Judging how good my understanding of Socrates is. Deciding wether capitalism or socialism is better. Considering the best activities to start learning history with. These things require judgment and some involve things that some people consider a "matter of opinion", "subjective" or "arbitrary" (which they often say when they find it hard to be objective, rather than because they have arguments that objective judgment of the matter is impossible). These issues are getting away from facts like how long an object is, whether it's made of wood, what shape it is, how heavy it is, whether it's flat, etc. They're different and trickier.