This is how psychologist Derald W. Sue, who's written two books on microaggressions, defines the term:
"The everyday slights, indignities, put downs and insults that people of color, women, LGBT populations or those who are marginalized experiences in their day-to-day interactions with people."  (The term, "microaggression" was first proposed by psychiatrist Chester M. Pierce, MD, in the 1970s )
As we understand what microaggression looks like, it should become clear that most often, it is unconscious (like the underlying bias). This can make it hard to see, let alone avoid. Indeed, what one may intend as a compliment, may be experienced by the recipient as a microaggression. It is very likely all of us received and delivered microaggressions. It seems unlikely anyone has died from receiving a microaggression, but the pain inflicted is cumulative. It has been likened to "death by a thousand cuts." 
A single microaggression might easily be overlooked or excused. But the cumulative effect of many of these, day in and day out can be crushing. There are some similarities with domestic violence, in that typically there are years of patterns of abuse which, when considered in isolation may appear to be relatively innocuous. But when considered as part of a pattern each instance is amplified for the recipient. Some researchers suggest microaggressions may be even more damaging than "overt racism" which is more easily recognized.