"The Olympic Charter explains that "the expression 'country' means an independent State recognized by the international community," and the IOC recognized Puerto Rico as such an entity in 1948. Although the United States granted the island the right to elect its own governor in the same year, that power is nothing like full independence. The U.S. Department of the Interior still classifies Puerto Rico as an "insular area" of the United States—a "jurisdiction that is neither a part of one ...

"The Olympic Charter explains that "the expression 'country' means an independent State recognized by the international community," and the IOC recognized Puerto Rico as such an entity in 1948. Although the United States granted the island the right to elect its own governor in the same year, that power is nothing like full independence. The U.S. Department of the Interior still classifies Puerto Rico as an "insular area" of the United States—a "jurisdiction that is neither a part of one of the several States nor a Federal district." But apparently the IOC considers insular areas sufficiently independent to participate in the games; the committee recognized the U.S. Virgin Islands in 1967, Guam in 1986, and American Samoa in 1987."

It's basically up to the discretion of the IOC, it's similar to the reasons that Israel & Palestine and China & Taiwan all have their own teams.