Neurons can hand each other information in the form of activity. A neuron tells another neuron to fire by releasing neurotransmitters, chemicals which stimulate them.
Neurons can essentially pass each other notes, but the only information the notes have is the type of paper it is, you could say the color of the note. But the neurons don't pass the same color of note to other neurons, nor is the color of the note necessarily important to the neuron itself. This seems very basic, but when you have many many many of these passing very basic units of information, combined with the fact that information coming from certain neurons must mean certain things (I.e. a signal coming from a pain receptor on your hand can only mean there is pain coming from a certain spot on your hand) you can get remarkably complicated signals and manipulate these signals in numerous ways.