Why is Gibbs free energy negative?
Gibbs free energy is negative for a spontaneous reaction (only). It can be positive as well, for reactions that are not spontaneous.
(If you are unsure of entropy, think of it as a measure of the random behaviour of the particles in the system. High entropy refers to a more random or chaotic state, such as a gas compared to a liquid. Processes in which entropy decreases tend not to occur in nature, unless there is a significant input of energy to cause them to take place.)
For a reaction run at constant temperature, it is defined as
If the free energy is negative, we are looking at changes in enthalpy and entropy that favour the process and it occurs spontaneously. This includes exothermic reactions in which the entropy increases, or exothermic reactions which have small decreases in entropy (as long as the temperature is relatively high), and endothermic reactions which are accompanied by large increases in entropy (like evaporation of water).
A positive free energy indicates a reaction that is not spontaneous; one that would have to be driven by an external input of energy, like the recharging of a battery.