The Maya Civilization—also called the Mayan civilization—is the general name archaeologists have given to several independent, loosely affiliated city states who shared a cultural heritage in terms of language, customs, dress, artistic style and material culture. They occupied the central American continent, including the southern parts of Mexico, Belize, Guatemala, El Salvador and Honduras, an area of about 150,000 square miles. In general, researchers tend to split the Maya into the Highland and Lowland Maya.
By the way, archaeologists prefer to use the term "Maya civilization" rather than the more common "Mayan civilization", leaving "Mayan" to refer to the language.
Highland and Lowland Maya
The Maya civilization covered an enormous area with a large variation of environments, economies, and growth of the civilization. Scholars address some of the Maya cultural variation by studying separate issues related to the climate and environment of the region. The Maya Highlands are the southern part of the Maya civilization, included the mountainous region in Mexico (particularly Chiapas state), Guatemala and Honduras.
The Maya Lowlands make up the northern segment of the Maya region, including Mexico's Yucatan peninsula, and adjacent parts of Guatemala and Belize. A Pacific coastal piedmont range north of the Soconusco had fertile soils, dense forests and mangrove swamps.
See Maya Lowlands and Maya Highlands for in-depth information.
The Maya civilization was certainly never an "empire", inasmuch as one person never ruled the entire region. During the Classic period, there were several strong kings at Tikal, Calakmul, Caracol and Dos Pilas, but none of them ever conquered the others. It's probably best to think of the Maya as a collection of independent city states, who shared some ritual and ceremonial practices, some architecture, some cultural objects. The city states traded with one another, and with the Olmec and Teotihuacan polities (at different times), and they also warred with one another from time to time.