The main reasons to separate the substances from its mixture are:
1. To remove the non-essential or impurities.
Churning milk to obtain butter:
2. To obtain the useful components by separating two substances.
Removing stones from the rice 
Now, we understand that we separate substances to remove harmful or non-essential substances from the mixture to get useful materials.  
Sometimes, we separate even useful components, in case we need to use them separately.
The substances to be separated can be in different sizes or materials. Or they may be in any three states of matter, i.e., solid, liquid, or gas.
How do we separate substances if they have different properties?
We use various methods to separate the substances and will see those methods in upcoming lessons.
Free image credits:
Mil and butter: