Russell Roberts attempts to explain why we trade in 1000 words. Let me try to be much more succinct:
We trade because buyers and sellers agree on a price which is respectively lower and higher than the value of the thing being traded.
That may sounds like a Zen koan, in that a price is usually denominated in a value of currency, e.g. dollars and cents. So how can a price be higher and lower? The answer is that the price is the same number. It is the value of the thing being traded which varies. In the eye of the buyer, the value of the thing is greater than the price. In the eye of the seller, the value of the thing is less than the price.
That is why we trade.