A common name is a term other than a specific epithet or scientific name which is used to refer to an organism. For example, “human” is a common name which refers to Homo sapiens. Common names tend to be easier to say and remember than scientific names, which is why they are so appealing; after all, everyone can remember “African Elephant,” but Loxodonta africana is a bit trickier to keep in mind, let alone spell.
Common names do come with some distinct disadvantages. For starters, unlike scientific names, they are not standardized, which means that the same common name may be applied to multiple organisms, or a single organism may have a plethora of common names. This can lead to confusion, whereas using a scientific name makes the identity of an organism under discussion very clear.
A common name can also be extremely broad, which may be a disadvantage as well. For example, trees in the genus Quercus are referred to commonly as “oaks,” but there are hundreds of trees in this genus. By just using the term “oak,” people avoid making a clear distinction, and this can be problematic. Different oaks grow in different areas, and exhibit different characteristics, and the use of a broad blanket term ignores this issue. Some attempts have been made to address this with more detailed common names, like California oak, black oak, and live oak, but these terms are not consistent or perfect.
The derivation of common names varies. Common names like cat, dog, and sheep have been around longer than the specific epithets for these organisms, and many of these names have ancient roots. Some modern common names are derived from scientific names, or vice-versa: narcissus, dahlia, and rhododendron are all common names, as well as the names for specific plant genera. In some cases, common names have been deliberately engineered to create a memorable name for an organism, and others have been refined from existing common names.
In some cases, an organism does not have a common name. This doesn't necessarily mean that the organism isn't common, merely that the organism is not well known to humans, well used by people, or considered valuable to people. In fact, many organisms without common names play vital ecological roles, they just haven't been harnessed in agriculture or daily life, so people are not familiar with them. Newly discovered organisms also tend to lack common names until one can be settled upon.