The Mississippian is the first geological epoch in the Carboniferous geological period. It began about 359 million years ago and ended 323.
The names Mississippian and Pennsylvanian are used in North America, because they match the strata there. Geologists from elsewhere mostly use just 'Carboniferous', or they use the official terms for stages, as defined by the International Commission for Stratigraphy.
During the Mississippian the sea level was high, and much of North America was covered by a shallow sea. The strata are mostly layers of marine limestones.