"Jaře" is the locative singluar form of "jaro." As I am learning too, I can't tell you exactly WHY the locative case is required, other than to suggest that "na" (in) hints at location -- we are saying "IN the spring."
Two of the seasons use "na" for "in" (spring and fall) and the other two (summer and winter) use "v" instead.
na jaře -- v létě -- na podzim -- v zimě
Essentially, the present continuous ("I am working") indicates an action that is happening now. The simple present ("I work"') describes an action that occurs often, regularly, or as a rountine. In this sentence, we are speaking about our regular practice of working in the garden during spring, so the simple present is used.