The Seminole Wars (there were three) were battles of groups of Native Americans who joined together (and were called Seminoles) fighting with the Spanish against the United States at first; later the Seminoles were pitted against the U.S. as American forces tried to take land from tribes settled in Florida.
Early on, most of the indigenous tribes of that area had already been driven out of Florida, killed, or taken by the Spanish to Cuba. Other Native Americans started to move east to Florida. Dissension arose because the Native American tribes wanted to keep their land, and the American engaged them to take the land, generally to push them to the west. Some treaties were signed, but specific tribes (i.e., the Mikasukee, and the Seminoles) did not align themselves with, for example, the Creek nation, and refused to be governed by a treaty that they had not agreed to.
The significance is probably two-fold. We see the United States taking land from the Native Americans, with aggression and all out fighting between the two sides. And ultimately, the U.S. controls Florida completely and the Seminoles are gone. After many years, and three separate wars, most of the Seminoles in Florida who had not already been captured and removed, were paid cash and moved out west. When the war was declared to be over, the few Seminoles remaining were generally left alone.
Though dates differ according to different military sources, the First Seminole Ware began around 1816, and the third war ended in 1858.