If you dissolve a salt in water and get an acid solution, such a salt is called acid salt.
If the salt dissolved in water gives a basic solution, we call that salt a basic salt.
If salt solution is neutral, it is a neutral salt.
You can drop a litmus paper in solution and determine of a salt is acidic, basic or neutral by looking at the color of litmus paper.
When a strong acid and strong base reacts, we have a neutral salt.
If strong acid react with weak base, we get acidic salt.
If strong base reacts with weak acid, it forms basic salt.
when weak base and weak acid reacts, we get either acidic or basic salt.
The reason for this is that,
when salt dissolve in water, the stronger species becomes dominant. So, if strong acid, then salt is acidic.
Strong base gives basic salt.
When both are strong, it's neutral.