The profit maximisation point is MR=MC. Below are the diagrams for the profit maximisation point for both monopoly and perfect competition markets. The profit maximisation point is the quantity and price level that the firm will produce at to ensure the most benefit. Before point X, MR is greater that MC thus profits will rise and rise. After point X, MC is greater than MR, thus firms do not see it profitable to produce after that point because they lose money.
For a monopolist, firms charge a price level higher than profit maximisation because it maximises producer surplus and consumers are still willing to purchase at that price level (See notes here). The quantity produced remains at Q1. For a firm in perfect competition, the level of output produced is at X and the price charged to consumers is P1, making the firm productively and allocatively efficient. For more notes, see here.
For more notes on perfect competition and monopoly markets, see here and here, respectively.