Nerf Balls were soft, sponge-like balls that came out in the 80's. They were available in big and small shapes and also as footballs and smaller tennis-type balls. They were very safe to play with.
Later on Nerf Balls came out with long tubes that you could use to shoot Nerf Balls at each other and later still they came with a bow and arrow type Nerf weapon.
I remember having a great time with them. The only bad thing was that they would wear down easily because they were so soft.