University of Miami law school professor Tamara Lave:

Before explaining what second degree murder means in Florida, it is helpful to understand why there are degrees of homicide. Distinguishing between first degree murder, second degree murder, and manslaughter is a way of differentiating between the culpability of defendants. The legislature believes that planning someone's death reflects a more dangerous and responsible killer than one who kills without planning it or it one who kills accidentally. Accordingly, there is also a difference in possible punishment. Defendants convicted of first degree murder can face the death penalty, but those convicted of second degree murder cannot. Similarly, defendants convicted of second degree murder face life in prison but those convicted of some level of manslaughter do not.

With that in mind Second degree murder in Florida is defined as follows: The unlawful killing of a human being, when perpetrated by any act imminently dangerous to another and evincing a depraved mind regardless of human life, although without any premeditated design to effect the death of any particular individual, is murder in the second degree and constitutes a felony of the first degree, punishable by imprisonment for a term of years not exceeding life or as provided in s. 775.082, s. 775.083, or s. 775.084

This is just a fancy way of saying that George Zimmerman is accused of killing Trayvon Martin unlawfully and without planning it in advance. The fact that the act must be imminently dangerous means that Zimmerman must have been doing something which was immediately dangerous instead of just possibly dangerous. Saying that he needs to evince a depraved heart is a way of saying that he acted without sufficient regard for human life. This is sometimes stated as a "hardness of heart." Shooting a gun into a crowded movie theater is one example of an act that shows a depraved heart.