The Seminole Indians are not an indigenous tribe or originally native to Florida but are an amalgamated group created by a series of historical events.
During the 17th and early 18th centuries, the area of Georgia formed a buffer between the Spanish and English colonies in the Americas. With the founding of a new English colony there in 1732, European expansion and political tensions brought increasing pressure on the native population. English immigration and demand for land pushed the tribes inland. Many more were displaced by the nearly incessant colonial warfare between European powers, during which traditional native rivalries were exploited in order to enlist them as allies.
Initially, great numbers of southeastern natives moved westward into Appalachia. But with only a handful of aboriginal natives left in Florida, most of their population having succumbed to European diseases, groups from the Lower Creek tribes began moving south. Spain encouraged these migrations as the Indian settlements would help to provide a buffer between Florida and the new British colony.
In addition to Creeks, Mikasuki, Yuchi, Oconee, and Yamassee other Miskogee and Hichiti speaking Indians found their way south. This population increased with the addition of runaway slaves and even some Europeans who found refuge among the Indians.
There is a Creek word ishi semoli which literally means “the people, whom the Sun God does not love,” an outcast or wanderer. But most likely the name Seminole comes from the Spanish word Cimarron, meaning roughly a wild runaway. This is also the origin of the word Maroon which was applied to the African slaves. By the end of the 18th century this mixture of various peoples became known collectively as the Seminoles. In the early 1800s, the United States government decided to relocate them from Florida to "Indian Territory" (present-day Oklahoma). You can learn more about the Second Seminole War and the Seminole incarceration period at the Castillo here.
Learn more about the Seminole history and culture at their Ah-Tah-Thi-Ki Museum.