There are a number of different barriers to entry that can allow monopolies to form. Different books will mention different barriers. Here are a few that I think are important:
Ownership of an important resource. For example, it can be impossible for a new water company to enter a market because the existing water company owns all the pipes used to move water around.
Patents and copyrights. Governments protect intellectual property by issuing patents and copyrights. This can make it impossible for new firms to enter a market. For example, Disney owns the rights to the Star Wars universe now and other firms cannot enter that market.
Government restrictions. There are many places where governments have set up rules that make it hard or even impossible for new firms to start up. For example, most governments grant monopolies to single cable companies in their area. This prevents other companies from offering cable TV services in a given area.
Start-up costs. Some kinds of business are very expensive to start. It is relatively easy for someone to start a small restaurant, but it is extremely expensive to start a new company building airplanes. This makes it hard for firms to get started in that market.
The major allocative difference between these two market types is that perfect competition brings about allocative efficiency and monopoly does not. This is because monopolies do not have to produce at the point where marginal costs equal the price for which the product is sold. Instead, they can produce less of a product than consumers want at a given price.
In terms of distributive efficiency, monopolies allow wealthier people to have a larger proportion of a given product than they would in perfect competition. This is because monopolies allow firms to charge higher prices for their products.