The reason it's called a birthday suit is it's the suit you were born in.
Well basically you were not born wearing a suit but instead every baby is born naked and the suit refers to your bare skin that you're born in.
The Birthday Suit is an informal term for the naked human body (as people are at birth).
The saying or term Birthday Suit was first recorded and the use of this phrase is in the mid-1700s.
It seems most likely that the phrase came originally from the style of dress that English kings would present themselves in on their birthdays.
Royal fashion statements would be made and noticed on birthdays. Reporters would call these birthday suits.
An example of how to use birthday suit in a sentence would be.
She came home and got into her birthday suit and went for a swim in her backyard pool.
Every time you get naked you are in your birthday suit as birthday suit is the naked skin you're born in.
All babies were born and are born wearing nothing but their skin which is their birthday suit.
So if you get naked or go skinny dipping etc then you're also in your birthday suit.
Just don't go out in public in your birthday suit as you can get arrested though unless you're on a nude beach.