Linguistics (the study of language) divides two major ways: spoken (called phonics) and written. Another major division is synchronic vs, diachronic—as the derivations of the terms imply, study of words as they change meaning, inflection, syntax, form, etc. through time (dia—chronic) and study of words as they work together in the same time frame (syn-chronic). In literary scholarship, diachronic linguists study how, for example, a word’s meaning changes from one century to the next—how does the word “servant” change meaning from the Latin meaning—“one who serves” through medieval and Renaissance times—“one who is loyal to a certain lord (his “servant”) to Victorian times—a domestic employee whose job is to “serve” food—to modern times—a person subservient to a stronger entity. This is, of course, an over-simple example of how words change through time, but it “serves” to demonstrate what is meant by studying linguistics “over time.”
An example of synchronic linguistics might be “pot”—while it means a cooking utensil, it also means (at the same time) marijuana, and “the chips to be competed for in a poker game.” Again, this is an over-simple example to demonstrate the meaning of “synchronic linguistics.”
In practicality, then the term “diachronic linguistics” means “the study of how language has changed and is changing over time, through the history of language development.” This linguist would be interested in how “thee” and “thou” changed to “you”, or why some words became contracted—“won’t, can’t,” etc.--or why the syntax of noun and modifier is different in English and French (red wine vs. vin rose); the synchronous linguistics would be interested in how words get their connotations—“whore,” “escort,” “streetwalker,” “prostitute,” “woman of the night,” etc., or “cop,” “police officer,” “flatfoot,” “fuzz,” etc., or the linguistic subtleties of placing an auxiliary clause in a sentence at the beginning vs. the end of the sentence. The diachronic linguist studies Chaucer and Shakespeare for their contributions to the growth of the English language. The synchronic linguist compares Hemingway’s sparse use of modifiers (adjectives and adverbs) with Joyce’s attempts to exhaust the English language.