First, it is more common to say that individual firms have market power, not that the industry as a whole has market power. Market power is the power of a firm or firms to set the prices at which they will sell their goods or services. In perfect competition, firms have no market power. They are price takers who cannot influence the price of their products. In other market structures, firms can have market power. They face downward sloping demand curves, not the flat demand curve that is present in perfect competition. Therefore, they can raise prices without losing all of their customers.
The major benefit that market power brings to firms in a given industry is the ability to make economic profit. In perfect competition, firms can never make economic profit. They are price takers and the price is driven down, through competition, as low as possible. But firms in other market structures can make economic profits either in the short term or possibly in the long term. They can convince enough customers that their product has no good substitutes to be able to raise prices and still make money. They can raise prices high enough to make economic profit. This is the major benefit of having market power.