As mentioned, a strong demense is a huge economic asset. Depending on how large a realm you control, your demense might supply everything from 25% to 75% of your income. Even starting out as the king of France with a mere two holdings, one's demense accounts for about half of one's income (if I remember correctly)
Beyond that, your demense is an important military asset. You'll usually be able to raise almost all levies in your demense, giving you a powerbase even in times where your vassals dislike you, for example in my current campaign as France, heir after heir got assassinated, and I finally ended up assassinated as well and thus had to live with the Kinslayer trait and a large number of rebellions, and my demense then contributed largely to my military force as it held stable throughout it all.
Beyond that, your demense is an important military asset. You'll usually be able to raise almost all levies in your demense, giving you a powerbase even in times where your vassals dislike you, for example in my current campaign as France, heir after heir got assassinated, and I finally ended up assassinated as well and thus had to live with the Kinslayer trait and a large number of rebellions, and my demense then contributed largely to my military force as it held stable throughout it all.