Onomasiology (from ὀνομάζω onomāzο 'to name', which in turn is from ὄνομα onoma 'name') is a branch of linguistics concerned with the question "how do you express X?" It is in fact most commonly understood as a branch of lexicology, the study of words (although some apply the term also to grammar and conversation).
Onomasiology, as a part of lexicology, starts from a concept which is taken to be prior
(i.e. an idea, an object, a quality, an activity etc.) and asks for its names. The opposite approach is known as semasiology: here one starts with a word and asks what it means, or what concepts the word refers to. Thus, an onomasiological question is, e.g., "what are the names for long, narrow pieces of potato that have been deep-fried?" (answers: french fries in the US, chips in the UK, etc.), while a semasiological question is, e.g., "what is the meaning of the term chips?" (answers: 'long, narrow pieces of potato that have been deep-fried' in the UK, 'slim slices of potatoes deep fried or baked until crisp' in the US).
Onomasiology can be carried out synchronically or diachronically, i.e. historically.
Onomasiology was initiated in the late 19th century, but it received its name only in 1902, when the Austrian linguist Adolf Zauner published his study on the body-part terminology in Romance languages. It was in Romance linguistic that the most important onomasiological works were written. Early linguists were basically interested in the Etymology, the word history, of the various expressions for that which was mostly a clearly-defined unchangeable concrete object or action. Later the Austrian linguists Rudolf Meringer and Hugo Schuchardt started the Wörter und Sachen movement, which emphasized that every study of a word needed to include the study of the object it denotes. It was also Schuchardt who underlined that the etymologist/onomasiologist, in tracing back the history of a word, needs to respect both the "dame phonétique" (prove the regularity of sound changes or explain irregularities) and the "dame sémantique" (justify semantic changes).