Atoms themselves are made up of smaller bits. There's a central bit called the nucleus and around that are lots of 'electrons'. Electrons are very important. They make lots of things happen. Without electrons things wouldn't dissolve, have a colour, conduct electricity, etc.
Static electricity is also to do with electrons.
So the electrons balance out the protons. This means the atom has no 'charge' - it's balanced. But you can remove electrons from or add electrons to atoms which means you've either got too many or too few electrons making atoms negative or positive. And just like opposite ends of magnets attract each other, so do opposite atoms. A negative atom will attract a positive one.