The average cost curve is u-shaped because costs reduce as you increase the output, up to a certain optimal point. From there, the costs begin rising as you increase the output.
To understand why this happens, you need to know what the average cost is. In economics, there are two types of costs: variable and fixed. Fixed costs are those expenses that remain the same. They include things like rent and bills for utilities. Variable costs keep on changing. Inputs are examples of variable costs. You may need more inputs as the demand increases.
Average cost is defined as the total costs (fixed costs + variable costs) divided by total output. As you increase the output and variable costs, the average cost reduces because the output adds value to the consumer.
Assume that you are in a room full of guests, and you give everyone a bottle of water because they are thirsty. You have paid for the venue, which can host a specific number of people (fixed cost). Your variable cost is the amount that you spend on water bottles. You may be forced to increase the water quantity as the event progresses. Buying more water for the guests helps them quench their thirst. Here, the average cost curve continues to slope downward.
However, there is a limit. After everybody is satisfied, the guests begin to waste the water. At this point, your average costs increase because the additional output doesn’t add any value to the consumer. The average cost curve suddenly starts sloping upward, forming a u-shape.