For everyone
I say this to my students all the time: the concept drives the computation. I only say it to students who are ready to hear it, those who either have some arithmetic under their belts or could if they tried. For students still fighting the battle to put in effort, it doesn't land yet. So what do I mean?
Following your nose
It means that understanding the concept tells you what to do to reach the answer. Math is a little like following your nose. But you need a great deal of experience before you can do it that way.
One of my professors described it like this: understanding math is like bacteria growing in a petri dish. Knowledge comes in splotches. As the splotches grow, they begin to bridge the gaps between them, and the whole colony gets stronger. That's what it's like to learn math.
Before algebra, it's mostly about arithmetic
There is plenty of concept before algebra. It's in the number line, in counting by twos and threes, in fractions (less than a whole), and in the idea that multiplication is fast addition and division is fast subtraction. But compared with all of mathematics, it's a small share. Mostly, the early years are about becoming proficient: adding, subtracting, multiplying, dividing, fractions, percents and decimals, and a long list of principles that you have to know cold.
Most students think all that is junk until they start understanding the concepts, and I think that's a fair reaction. It's a lot of stuff. It's not junk, though. It's the equipment you need.
Then comes X
Algebra introduces a new idea: you don't need to know a number's value to work with it. You can name it, usually X, and treat it as a number whose value you haven't found yet. Everything you learned in arithmetic now gets applied to that unknown. It's a real leap, and you have to take it partly on faith that all that "junk" will pay off. It will, and it matters when you're competing for a job with others who did the work.
Once the computation is solid, you're ready to think in concepts. The two support each other: computation supports the concepts, and applying the concepts through computation makes the computation stick. That's what modeling situations with math means. And the rabbit hole goes very deep, with branches that have branches.
Why it matters beyond math class
Math trains the mind to think with clarity and relevance, and to see things as they are, not as intuition suggests they are. That carries into life. It also makes us harder to manipulate. When an insurance company says "we take care of you like no other," what does that actually mean? Nothing. Think about it.
Two things to leave you with. From Arthur Conan Doyle's Sherlock Holmes: "Once you eliminate the impossible, whatever remains, however improbable, must be the truth." And a simple one: if it doesn't make sense, it isn't true.