Edwards first seeks to define true religion, saying, "true religion, in great part, consists in holy affections." He defines the affections in this way: "The affections are no other than the more vigorous and sensible exercises of the inclination and will of the soul." He bases this definition on the understand that the human soul has two faculties, one of which he terms understanding. This is the faculty that allows the human soul to discern, view and judge. The second faculty he terms inclination or will or heart. It is this one that allows the soul not to just perceive and view things, but to incline or disincline it. Holy affections are those that are distinguished by "vigorous exercise of the inclination and will towards divine objects."
Read Tim Challies' remarks, it is well worth reading.