for the better（固定短语）意思是“好转,向好的方向发展；变好”，“change for the better”意思是：为了更好而改变。可以理解为：变好；向好的方面变化。
1. I am happy to say that the patient has taken a turn for the better, last evening it was touch and go whether he would survive the night.
2. The situation is now so bad that any change is likely to be a change for the better.
3. The situation is now so bad that any change is probable to be a change for the better.
4. I trust that things will take a turn for the better in the near future.
The doctor felt that having a few days' rest would be for the better．
The world situation is changing for the better．
His state of health has changed for the better recently．