A monopoly is a relatively simple market structure. One firm is the single producer for the market, or serves the majority of customers. For this to occur there must be some kind of barrier which stops other firms from competing with that firm, such as legal protection like a patent, or large economies of scale. There also must be no close substitutes available for the product. Because no new firms can enter the market, a monopoly company can sustain abnormal profits in the long run. In practice, in the UK any company which serves 25% or more of the market is classified as a monopoly. A good example could be Google as a search engine, or National Rail which owns train lines.
Monopolistic competition, whilst similar in name, is a very different type of market structure. Here, there are many firms and few barriers to entry. These many firms all produce similar, but slightly different products (known as differentiated). These slight differences allow each firm to charge different prices, depending on their product. In the long run, firms in monopolistic markets cannot make abnormal profits. If they do in the short run, new firms will enter the market, competing away any abnormal profit. Good examples for monopolisticly competitive markets are the restaurant industry, hotels, and clothing companies.