There are essentially two kinds of clouds, layered clouds and convective clouds. Layered clouds are clouds that appear high in the sky. Convective clouds are the kind that are closer to the earth. It is important to note that the height of a cloud is calculated based on the space between the base of the cloud and the earth, not the height of the cloud itself. However, altitude is not the only way to categorize clouds.
In 1802 Luke Howard presented a system to the Askesian Society, a debating club for scientific thinkers that was established in England in the late 1700's. Howard, who has been called "The Godfather of Clouds," created the four major cloud categories by which we still assess cloud formations today. The four major types of cloud formation, as per Luke Howard's system, are cumulus, stratus, nimbus and cirrus.
The name cumulus comes from Latin and means "pile" or "heap." A cumulus cloud formation is marked by vertical development of the cloud as well as clearly defined edges. These are the types of clouds that look like puffy balls of cotton. Cumulus clouds often appear during fair weather. However, they can be precursors to severe weather.
A stratus cloud formation is a uniform layer of clouds that have a consistent base. Stratus clouds often bring light, steady precipitation such as drizzling rain. These clouds often appear to be flat, featureless, and hazy. They are low to the ground and often gray in color.
Nimbus is actually the word for "cloud" in Latin. Nimbus clouds are precipitation-producing clouds. The nimbus category is often combined with other categories to indicate storm conditions. Nimbo- is used as a prefix and -nimbus is used as a suffix to create such combinations. A nimbostratus cloud formation, for an example with the prefix, is a stratus cloud that is precipitating. A cumulonimbus cloud, for an example with the suffix, is a precipitating cumulus cloud.
Cirrus clouds are clouds that form the highest in the sky. A cirrus cloud formation will appear in the coldest region of the troposphere. They appear from the ground to be made of long, thin strands. They are sometimes described as wispy.
These are the four basic cloud formation families. As the earth's sky is a very interesting space, the clouds rarely keep to just one classification. In fact, it is quite common for clouds to be classified under more than one of these major cloud families such as in the examples given of the nimbostratus and the cumulonimbus.