Competitive markets are where the supply of stuff created equals the demand of that stuff which is bought up.
You have competitive markets when firms are price takers, not price makers, which means they have to set prices based on the market. Because competition will undercut your price if too high.
When supply = demand, we’re at equilibrium. Nobody can undercut anyone anymore, and all is right in the world of buyers and sellers.
In the real world, competitive markets are obvious. Sellers that are working hard to get buyers by slashing prices, differentiating their products, and building what we all love to hate and hate to love: brand loyalty. But there are also “perfectly competitive markets,” which is a theoretical, fairytale land where all products are exactly the same, all the prices are the same, and entering and exiting the market is no skin off your teeth. In both cases, firms are price takers.
In non-competitive markets, firms are price makers. A monopoly is a good example of a non-competitive market, because by definition, a monopolist is a firm that has a market all to themselves. What if there was only one supplier of smartphones in the world? That firm would be a monopoly, and it could raise the prices on all the smartphones. Sure, fewer smartphones would be bought, but the monopolist would actually make more money doing this (so they would, of course).
You have non-competitive markets when firms are more incentivized to stay away from equilibrium where supply equals demand, because that’s not where the money’s at when you’re a price maker.