When things are done separately, they are done one after the other, or in a different place from each other.
Doing things separately can make people think of organization or special treatment.
Examples:
I will eat my vegetables separately from my meat.
We will go to the store separately.
She likes to do her homework separately from her brother.
I will wear my shoes and socks separately today.
The cats eat separately because they don't like each other.
We will take the test separately so we don't cheat.