Rand defines capitalism as follows: “Capitalism is a social system based on the recognition of individual rights, including property rights, in which all property is privately owned.” (Rand, Ayn, Capitalism the Unknown Ideal). In such a system initiation of physical force is banned from human relationships because of the emphasis on the protection of individual rights. No individual or group may initiate the use of physical force against another. There is no coercion. Relationships are voluntary. Hence, no exploitation, no fraud, no theft, no slavery is permitted—because each of these things requires the initiation of physical force.
This does not mean that force is not possible, but rather that force is legally banned from human relationships. The government, under a capitalist system, has the sole responsibility to protect individual rights.
Since it would be redundant to restate her full case here, I will provide just some highlights and identify a few common misconceptions. For a fuller treatment of the subject, I strongly recommend reading Capitalism the Unknown Ideal.
First, note that capitalism is defined as a “social system based on the recognition of individual rights.” Rand defined things in terms of essentials. She worked to identify the most significant, most fundamental distinguishing characteristic of a thing when developing a definition. Note that capitalism is not defined as a “system of competition,” a “market driven system,” or even the “the system that provides the greatest good for the greatest number.” While these things may be true, they are not the critical distinguishing characteristic. The protection of rights is the distinguishing characteristic.
Second, when a non-essential characteristic is used to define capitalism, lots of questions become overly complex. For example, how can a free market automatically guarantee protection of individual rights? It cannot, unless the free market arises naturally as a consequence of capitalism—the system that protects individual rights. Most of the arguments leveled against capitalism use the straw man attack: Capitalism is X. X is bad. Therefore, capitalism is bad. If X is anything other than “a social system that based on the recognition of individual rights…” the argument is using a non-essential characteristic to define and attack capitalism.
Third, a key to understanding capitalism is to recognize that in practice it is a system that involved voluntary trade (no force, no coercion, no fraud, no deception, no theft, no exploitation, no slavery). Within a capitalist system each individual is free to trade (or not trade) with anyone else, and the role of the government is merely to ensure that individuals or groups who initiate force are punished and the rights of the individual are protected. Note, the individual—not any group—is the appropriate unit of a society. Also note that the government is the servant of the people not the other way around.
Finally, the unique achievement of the United States was the explicit protection of individual rights (See the US Constitution). This protection of individual rights led to the sudden dramatic and undeniable prosperity in the US and abroad—directly to the extent that capitalism was allowed to spread. Although the word was originally used pejoratively (https://www.libertarianism.org/encyclopedia/capitalism) capitalism currently has a neutral status to most people—instead of the elevated status and honored it deserves.