A microbrewery is defined (in the U.S.) as a brewery that brews beer for external consumption and has annual output of less than 15,000 barrels. A microbrew, therefore, is any beer brewed by a microbrewery.
The term has fallen out of favor in recent years. As smaller, "artisinal" brewers became larger (e.g., Samuel Adams, Sierra Nevada) a new way to distinguish these sorts of brewers from large, industrial brewers (Anheuser-Busch et al.) was needed. Craft beer and Craft brewer are now the more popular terms.