A person is a person, but a passport is just a piece of paper. There are lots of reasons why a person would want to have several of these pieces of paper.
1. Second passports can save your life. People have been persecuted and without a second passport they and their families could not flee.
2. Second passports can protect your assets. Many people use a second passport for offshore banking, in order to protect their assets from greedy governments.
3. Second passports allow greater freedom of movement. The UN declaration on the rights of man states that travel is a human right. Having only one passport can limit your travel, depending upon which country issued it. For instance, people traveling on an American passport would have a hard time traveling to Cuba, or Myanmar.
4. Second passports provide camoflauge from the acts of one's government. If America goes to war with Iraq, traveling on an American passport in certain countries or situations is likely to be very dangerous.