A hard nut to crack without much context. But my educated guess would be that it has to do with "a spell", a time in life which someone has interest or tries his hand at something. For example, someone retires and then has some free time, then he/she develops interest for arts, it´s his season art (that is, it´s his season for art.)
It could be other seasonal time as well, as in the summer, in the school holiday period, etc.
It´s a hunch of mine here, though.