The brain is an organ made up of cells. This is just like any other tissue or organ in the body is made up of specialized cells. The heart is composed of heart cells that are found nowhere else in the body, the liver of liver cells, and so it is with the brain.
The most famous type of brain cell is the neuron. Actually there are hundreds of different types of neuron but we will ignore that here. Neurons differ from all other cells in the body because they send out projections to meet each other to form a complicated network capable of fast and flexible communication. All cells are capable of communicating with each other at some level, but we are talking about something much faster and more flexible found only in cells of the nervous system.
For a long time people thought that the cells of the brain (and the rest of the nervous system) were all joined up in a huge net; this was called the 'reticular hypothesis'. But towards the end of the 19th century it became clear that they don't actually join up, and that each neuron was separate and a "fully autonomous physiological canton" (Cajal, 1888). Thus was born the neuron hypothesis.
(We will ignore, for the moment, all brain cells that are not neurons - although it turns out that this is probably a big mistake.)
So, the neuron sends out information to other neurons down a thick-ish fibre called an 'axon', and gathers information from its surroundings, through thin thread-like projections called 'dendrites'. Dendrites and axons are usually, but not always, on opposite sides of the cell body which, if you look at pictures, is the 'blob' in the middle.
The most obvious sort of activity that is carried away from the neuron by the axon is the action potential, which is a spike of electrochemical activity. These spikes, or clicks, are the usual form in which information is encoded and moved around the brain. In the places where an outgoing axon gets close to, but never quite touches, a receiving dendrite, there is a special structure that controls the passage of information across the gap, or cleft, called the synapse.
You won't find this in many textbooks, but my money, and all the smart money is on the synapse (which is not yet that well understood) being the key to much of the really clever stuff that happens in the brain.
From: Martin’s Vastly Oversimplified and Woefully Incomplete Guide to Everything in the Brain as featured on the Brainsex website.