Technically, the German Empire was a "federal monarchy" - that is, a federation of each monarchical state (Prussia, Bavaria, Saxony, etc.), each of which was sovereign in its own right. So the King of Bavaria maintained his aristocratic rule over Bavaria, was its sovereign, had some executive freedom. The constituent kingdoms of the German Empire retained a significant amount of independence (at least more than, say, US states during the same period) - for example, they maintained their own armies (if you read World War I narratives from Germans, you'll hear their regiments or divisions referred to based on their kingdom of origin... for example, I believe Ernst Jünger was from a "Hanoverian Rifles" regiment). So the Kings maintained an active executive role in the administration of their kingdoms and were fairly important (the German Empire, while not as liberal as Britain, still wasn't an absolute monarchy, so I don't want to overstate the importance of the German kings; Germany was a modern state with an elected legislature that played a critical role in determining policy).

Abdication I know a little less about, so I can't give specific answers, but I believe it was essentially due to a wave of revolutionary, anti-monarchical sentiment that swept the nation following the humiliation at Versailles. The Kaiser fled to the Netherlands, for example, to avoid meeting the fate of Cousin Nicky at the hands of German socialists. The Sparticus movement in Bavaria nearly broke Bayern off from the rest of the nation as a socialist state. These were not safe times for monarchs to cling to power, to say the least.