On the graph related to the firms topic, why does the marginal cost curve meet the average cost curve at its lowest point.

The marginal cost is the cost of producing an additional unit, whilst the average cost is the average cost of producing each unit. If the marginal cost is lower than the average cost then the average cost will decrease. If the marginal cost is higher than the average cost then the average cost will increase. Therefore, as the marginal cost cuts the average cost curve from below the marginal cost has consistently been lower than the average cost, meaning that the average cost has been decreasing.
As, due to diminishing marginal productivity, the marginal cost will then increase to be higher than average cost, the point where MC=AC is the point just before the marginal cost is higher than the average cost. Therefore, the average cost will increase from this point and thus when MC=AC, average cost is at its minimum.