What is the "terrible thing, the almost impossible thing"?

The whole quote pretty much explains it:

“The terrible thing, the almost impossible thing, is to hand over your whole self--all your wishes and precautions--to Christ. But it is far easier than what we are all trying to do instead. For what we are trying to do is to remain what we call "ourselves," to keep personal happiness as our great aim in life, and yet at the same time be "good.”