A neuron is the basic cellular building block of the brain and nervous system. It is the thing within your body that acts as the messenger and sends information to and from the brain and other parts of the body. It allows certain messages to be sent, so that you can move and act in the ways that you intend.
A neuron is different from a nerve, which may be a more recognizable term. Nerves are actually groups of neurons that transmit information throughout the rest of the body. Everyone has nerves, in their arms, legs, etc., which are simply bundles of neurons.
A neuron has certain special structures that make it different from other cells, but allow it to function as this messenger within your body.
First, there is the soma, or the cell body. This is the central area of the neuron that makes it just like other cells. It contains all the different structures that different cells in your body contain, such as the nucleus containing DNA, the mitochondria, etc. The important thing to remember is that the soma is your cell body, or the center of the neuron.
Outside of the soma are these little branching, tree-like structures, called dendrites.
These aspects of the neuron, that branch off into lots of smaller parts, receive information from other neurons. This is the receiving section of the neuron. It takes in messages that other cells and neurons send to it, and then transmits it to other cells.
The axon starts at the cell body, in the area called the axon hillock, and extends all the way to a button-like structure at the end, which is called the axon terminal.
Now, the axon essentially transmits an electrical impulse from within the cell, starting at the dendrites and the cell body, all the way across the tail and out to other neurons that might be attached to it. It's sort of like an electrical wire, and just like with an electrical wire, the transmission of that electrical signal can be improved by insulating it, or putting something around that axon to make the message transmit faster.
This is true in certain neurons within the brain itself; they have what is called a myelin sheath. The myelin sheath is an insulating layer of fat, called glial cells, which wraps around the axon and makes that electrical impulse shoot faster through the axon, down to other neurons that might be attached.
Source: This work is adapted from Sophia author Erick Taggart.