The basic reason for this is the fact that, after a certain point, returns tend to diminish as output goes up. This is called the law of diminishing returns.
At first, marginal costs tend to go down as production increases. This is typically because of specialization in the labor force. For example, if you have 1 person making shirts, they have to do the whole job. But then if you add another person, one can cut and the other can sew. If you add another, one can cut sleeves, another cuts the body, and the third sews. In this way, you actually reduce your marginal costs as you add output.
At some point, however, the law of diminishing returns sets in. Once you have the right number of workers, making more shirts ends up costing you more because you have to pay overtime, for example. This could also happen because you have to hire another person to cut sleeves but that doesn't really help much because it's the short run and the number of sewing machines is fixed and the person sewing can't really keep up with all the cut pieces coming at them.
So, marginal costs will tend to go down at first as specialization helps you make more, but they will go back up as the law of diminishing returns kicks in.
Marginal cost is the cost incurred when making an extra unit and it is also affected by the principle of variable proportions. Marginal cost is derived solely from variable costs and follows a similar U-shape. The marginal cost decreases in the beginning but reaches a maximum point when it starts increasing.
In the short run, a firm has the capacity to increase its output by increasing the use of the variable factors while holding the fixed factors constant. Thus, the principle of variable proportions takes effect because at least one factor remains constant.
The variable costs that affect the marginal cost will initially increase the returns. However, an optimum point will be reached where any further increase of the variable factor will not increase the returns. Further increments of the variable factors/ marginal cost past the optimum point will have the effect of diminishing returns.
Thus, the marginal cost curve, like the variable cost curve will first slope downwards until a constant point before sloping upwards and forming a U-shaped curve.