There are different reasons for different campaigns. His first initial campaign against the Jurched to the south was soon after he had unified the steppe people. Jack Weatherford summarizes it well in Genghis Khan and the Making of the Modern World:
"The position of a steppe khan rested on his ability to win in a battle and to ensure a steady supply of trade goods. Usually the two coincided when battlefield victory provided an opportunity to loot the defeated. Genghis Khan's unprecedented success in defeating and uniting all the tribes had the inadvertent consequence of ending the looting and stifling the flow of goods. Since all manufactured goods originated in the south, Genghis Khan could either offer allegiance to one of the southern rulers and receive goods as a vassal warrior, or he could attack them and seize the goods."
Another short conquest against a Siberian tribe began when the tribe stopped supplying tribute to Genghis Khan. He sent envoys to collect tribute and the chieftain, a woman, captured the envoys. He sent a favored general and a detachment of troops but they were in foreign forested lands and were ambushed and killed. After this Genghis Khan gathered a much larger force and invaded them, freeing their envoys and capturing the tribe as prisoners.
Another conquest against the Muslim Khwarizm sultanate was due to hostile relations in trade. Genghis Khan offered to open trade between his and their peoples and their sultan agreed. He sent a caravan of of 450 merchants along with luxury items earned from previous campaigns but a local governor of the Khwarizm sultanate killed the caravan and took their goods. Genghis Khan was angered by this so he sent envoys, demanding that the local governor be punished but the sultan offensively rebuked him and the envoys were either killed or sent back to Genghis Khan with mutilated faces. This was the casus belli that started a brutal campaign against the Khwarizm sultanate.