Perhaps the simplest explanation of lexicography is that it is a scholarly discipline that involves compiling, writing, or editing dictionaries. Lexicography is widely considered an independent scholarly discipline, though it is a subfield within linguistics.
Many consider lexicography to be divided into two related areas. The act of writing, or editing dictionaries is known as Practical Lexicography. The analysis or description of the vocabulary of a particular language, and the meaning that links certain words to others in a dictionary, is known as Theoretical Lexicography. Theoretical Lexicography is particularly concerned with developing theories regarding the structural and semantic relationships among words in the dictionary. Since it involves theoretical analysis of the lexicon, Theoretical Lexicography is also known as Metalexicography.
In order to better understand lexicography, it may help to know what a lexicon is. Lexicon is a term used in linguistics to indicate the archive of lexemes. Lexemes are abstract, minimal units in a language that link related forms of a word together. For example, the words fly, flight, flew, flying, and so on, are all morphologic variations of the lexeme fly. Fly is the lexeme because it is the base from which these word variations arise.
Lexemes, then, make up a lexicon which is the collection of word meanings in a given language. In a dictionary, the lexemes, sometimes loosely referred to as word stems, are provided first and followed by variations of the base word. As we can see when we read a dictionary, the lexicon also deals with the area of linguistics known as semantics. Semantics refers to the aspects of meaning that are expressed in a language, and of course, in the vocabulary items of which a language is comprised.
In addition to providing data on the morphology and semantics of a lexeme, the dictionary also provides structural information regarding the root of the word, and historical information regarding the evolution of the word into its modern-day form. This is known as etymology.
A lexicographer is concerned with what words are, what they mean, how the vocabulary of a language is structured, how speakers of the language use and understand the words, how the words evolved, and what relationships exist between words. This is the information a lexicographer compiles when creating a dictionary.
So, a lexicographer is a linguist whose specific expertise is in writing dictionaries. Lexicography, with all its interrelated concepts, and its links to other areas of linguistics, is the specific area of scholarly work devoted to these concepts.