There are two major cropping seasons in India, namely,
Kharif and Rabi.
The Kharif season is during the south-west monsoon (July-October). During this season, agricultural activities take place both in rain-fed areas and irrigated areas. The Rabi season is during the winter months, when agricultural activities take place only in the irrigated areas.
Kharif (variously spelt including as Khariff) season would generally cover months of summer and rains (sown during April-July, and harvested by October). Most important Kharif crop is paddy. Rabi crops are generally sown between October to February and harvested by June. Most important Rabi crop is wheat. With expansion of irrigation and green revolution, traditional pattern of cultivation has changed in India, still paddy and wheat remain the major Kharif and Rabi crops respectively. Other Kharif crops include sugarcane, groundnuts, maize, and a variety of pulses. Other Rabi crops include barley and a variety of oil seeds. As regards Jaiyaj crops, I am not sure, but they may denote crops sown and grown between months of gap arising between Kharif and Rabi crops or vice versa.