Atoms, as we know them, are composed of protons and electrons, which are held together with a bonding force known as electromagnetism.
Electromagnetism occurs because protons have a positive charge and electrons have a negative charge, and hence, the two opposites attract each other, binding the two together to form an atom.
Scientists believe that without the electromagnetic forces, matter couldn't exist, and it would just disintegrate and dissolve into nothingness. Electromagnetism is literally the bonding glue that holds all of existence into a form of tangible matter.
If you've ever wondered why you can feel matter, scientists believe that this is electromagnetic force at its finest. Since electrons repel each other, you can feel the two negative forces clashing at a molecular level. This is what you feel when tapping on a hard surface, like on a table.