Linguistics is simply the study of language. The prefix micro refers to small, and macro refers to large. Microlinguistics refers to how small changes in language evolved and affect the sound and look of language. For example: there, they're, and their all sound the same but have small changes in the way they are spelled. Microlinguistics also looks at the way words sound (phonetics), the organization of those sounds (phonology), and how words are formed (morphology) to name a few. Microlinguistics is often not interested in the meaning of words as much as the way the word sounds or is formed and is often represented at the individual level.
On the other hand, macrolinguistics refers to how language and society interact, specifically how social factors can influence the use of language in the larger society. Macrolinguistics often compares languages across counties or cultures, the change of language overtime, or other large outside societal influences.