Formations are the fundamental unit of stratigraphy, the branch of geology the studies sedimentary sequences. A formation is a volume or body of rock which shows a consistent and homogeneous set of lithologies that allow to distinguish it from the neighboring sedimentary rocks and that can be mapped in geological maps. A formation occupies a specific position in the stratigraphy of a region and its lithologies reflect the sedimentary environment where it formed. Formations can be dated through the recognition of fossils within them or by radiometric dating of minerals containing radioactive elements (for example, tephra layers). The distinction of a sedimentary sequence in formations is, thus, the basis to recognize the sequence of events that occurred in geological times in a region.

Why defining formations?
Sedimentary rocks are sequences of layers of different rocks that alternate at scales ranging from some centimeters to several meters. Distinguishing and defining each layer in sequences that typically show thousands of layers is impractical and makes impossible to represent sedimentary rocks in geological maps. Defining a formation solves this problem, since formations divide sedimentary sequences in sets of strata that can be considered homogeneous at the scales of a sedimentary sequence (tens of meters to kilometers). In this sense, formations represent the first-order subdivision of sedimentary sequences which can be several kilometers thick and that can be represented on geological maps. 

Defining formations
Formations are defined on a lithologic basis (rock types, sedimentary structures, fossils), since we have to recognize them in the field with no other equipment than a hammer or a hand lens. A formation can be distinguished based on the recognition of a volume of rock that internally shows specific features that make it different from the surrounding rocks. Here is an example:

The slider above shows a sequence of sedimentary rocks from Walnut Canyon, Arizona. Geologists working in the area have distinguished the sequence in three formations. From top to bottom: the Kaibab Limestone, the Toroweap Formation, and the Coconino Sandstone. As you can see, this distinction divides the sedimentary sequence in internally homogeneous sets of layers, each of them showing characteristic structures and features. For example, the Coconino Sandstone show cross-bedded sandstones that differ from the overlying Toroweap Formation, consisting of gypsum-bearing shales with sandstone layers [BLOG POST]. Each of these formations corresponds to a specific stratigraphic age (the geologic age of deposition) and a well-defined sedimentary environment, reconstructed based on their sedimentary facies and fossil content. The formal designation of a formation also includes the definition of a stratotype or type section, which is an outcrop which exposes a complete section through the formation. In case such a good exposure is missing, several reference section can be defined. 

Naming formations
Geological formations typically have characteristic, unique names that denote some of their prominent features and/or the area where they were first defined. Sticking to the example above, Kaibab Limestone is named after the Kaibab Plateau, in Arizona, and ‘Limestone’, since it contains thick limestone layers. However, this does not indicate that limestones are the only rocks present within the Kaibab Limestone, which contains also dolomites, shales, and sandstones. It simply means that it is the most characteristic rock within this formation. In this sense, a formation name is a sort of nickname for a sequence of rocks. Similarly, the Toroweap Formation is named after the Toroweap Overlook and the Coconino Sandstone after Coconino County, Arizona. 

Formations of non-sedimentary rocks (lithodemes)
The definition of formations is based on the principles of stratigraphy and relates, hence, to sedimentary rocks or, at worst, to low-grade metamorphic rocks that well preserve their original sedimentary features. Other rock types, like igneous rocks, medium-high grade metamorphic rocks, or strongly deformed rocks, do not respect the principles of stratigraphy (in particular the law of superposition) and cannot be considered formations, but they are still distinguishable at map scale. In this case, they are considered lithodemes, non-sedimentary rock bodies that can be mapped.