The previous answerer is right in the sense that profits will be maximized and losses will be minimized when MC = MR.
You should, of course, be aware that there is nothing that says MC will always equal MR. So in that sense, your question is probably not stated exactly as you want it to be. I think what you are really asking is why SHOULD MC equal MR.
Basically speaking, the reason it should is because when MC is greater than MR, your firm loses money. When MC is less than MR, you are making money, but you aren't making as much as you could be. In that case, you would want to increase production until MC = MR. At that point, you'd make the maximum possible profit.
I believe in the question mc refers to marginal cost and mr refers to marginal revenue.
Marginal cost and Marginal revenue do not always equal. Marginal cost is dependent on the nature of cost in relation to marginal increase in quantity produced and offered for sale. Typically the behavior of marginal cost in relation to production quantity is represented graphically by a U-shaped curve.
Marginal revenue represents the increase in revenue of a firm for unit increase in quantity sold. Marginal revenue is dependent primarily on the demand curve. Typically, the marginal revenue in relation to production quantity is represented graphically by a downward sloping curve. However, for a firm operating in perfectly competitive market the marginal revenue curve is a horizontal straight line representing the market equilibrium price.
Marginal cost is equal to marginal revenue of a firm only when the firm produces at a level which maximizes the profits of the firm. If firm produces at a level which is 1 unit less than this, the firm looses the opportunity to increase its profit by an amount equal to marginal revenue less marginal cost. And if the firm sells more quantity then the quantity qt which marginal cost equals marginal revenue, the increase in cost is more than increase in revenue, leading to reduction in total profit.
mc equals mr to maximize profits.