These familiar prefixes (micro=very small; macro=very large) differentiate two approaches to the study of languages. The micro-linguist is interested in how small changes in a distinct word or other linguistic element may offer clues to larger trends: for example, how did “thou thee thy thine” become “you, you, your, yours” in modern English? Or how did contractions form (wouldn’t, won’t, can’t, doesn’t, etc.) evolve? These shifts in specific areas might offer clues to how language works—what forces are at work?
The macro-linguist, on the other hand, studies major changes in language from outside forces—the Latin language influence on English came from the Roman Empire’s expansion, for example. Look at how these two approach work together: The macro-linguist notes that the Norman Invasion brought French to the English; the micro-linguist, wondering why cow-meat is called beef, sheep-meat is called mutton, pig-meat is called pork, etc., notes that the French word for cow is “boeuf,” the French word for sheep is “mouton,” the French word for pig is “porque.” Together the linguists realize that the French invaders, whose servants were the conquered English peasants, ordered their meals using the French words, so the food names that the servants got used to were the French terms, and entered the English language that way.
Microlinguistics deals with phonetics, grammar, etc. on the individual example level; Macrolinguistics deals with comparative studies among languages, language families, large influences on language development.