From Wikipedia

Engineering An Empire: The Maya

• Ceremonial platforms were commonly limestone platforms of typically less than four meters in height where public ceremonies and religious rites were performed. Constructed in the fashion of a typical foundation platform, these were often accented by carved figures, altars and perhaps tzompantli, a stake used to display the heads of victims or defeated Mesoamerican ballgame opponents.
• Palaces were large and often highly decorated, and usually sat close to the center of a city and housed the population's elite. Any exceedingly large royal palace, or one consisting of many chambers on different levels might be referred to as an acropolis. However, often these were one-story and consisted of many small chambers and typically at least one interior courtyard; these structures appear to take into account the needed functionality required of a residence, as well as the decoration required for their inhabitants stature.
• E-Groups are specific structural configurations present at a number of centers in the Maya area. These complexes are oriented and aligned according to specific astronomical events (primarily the sun’s solstices and equinoxes) and are thought to have been observatories. These structures are usually accompanied by iconographic reliefs that tie astronomical observation into general Maya mythology. The structural complex is named for Group E at Uaxactun, the first documented in Mesoamerica.

Temple of the Cross at Palenque; note the intricate roof comb and corbeled arch

• Pyramids and temples. Often the most important religious temples sat atop the towering Maya pyramids, presumably as the closest place to the heavens. While recent discoveries point toward the extensive use of pyramids as tombs, the temples themselves seem to rarely, if ever, contain burials. Residing atop the pyramids, some of over two-hundred feet, such as that at El Mirador, the temples were impressive and decorated structures themselves. Commonly topped with a roof comb, or superficial grandiose wall, these temples might have served as a type of propaganda. As they were often the only structure in a Maya city to exceed the height of the surrounding jungle, the roof combs atop the temples were often carved with representations of rulers that could be seen from vast distances.
• Observatories. The Maya were keen astronomers and had mapped out the phases of celestial objects, especially the Moon and Venus. Many temples have doorways and other features aligning to celestial events. Round temples, often dedicated to Kukulcan, are perhaps those most often described as "observatories" by modern ruin tour-guides, but there is no evidence that they were so used exclusively, and temple pyramids of other shapes may well have been used for observation as well.
• Ball courts. As an integral aspect of the Mesoamerican lifestyle, the courts for their ritual ball-game were constructed throughout the Maya realm and often on a grand scale. Enclosed on two sides by stepped ramps that led to ceremonial platforms or small temples, the ball court itself was of a capital "I" shape and could be found in all but the smallest of Maya cities.