Neurons carry out their specialized functions of communication and integration because their outer cell membrane has special properties. The cell membrane separates the inside of a cell (all cells, not just neurons) from the outside, and all chemicals that get into and out of the cell must go thorough it. As in all cells, the cell membrane of a neuron is polarized. This means that there is an electrical difference across the cell membrane. The polarization of a cell can be measured by putting a very thin electrode inside a cell, as illustrated in Figure 3. (These electrodes are usually glass tubes tapered to a very fine point, about 1 um thick. Such points are barely visible with a light microscope.)
A voltmeter between this electrode inside the cell and another one in the fluid outside the cell shows that the inside of the cell is negative relative to the outside. In a neuron, this electrical difference is called the resting potential. The "typical" neuron has a resting potential of about -70 mV (about 1/20 of what a flashlight battery produces). The inside is negative relative to the outside.
To understand polarization, think of a flashlight battery. It has a + pole (the button at one end), which is positive relative to the - pole (the flat surface at the other end). Imagine that the cell membrane has lots of tiny batteries in it, with the positive button poles on the outside of the cell membrane and the flat negative pole inside, as illustrated in Figure 4 below. This would make the inside of the cell negative relative to the outside.
Of course, the cell membrane doesn't really have little batteries in it. The polarization is produced by chemically driven "pumps". They push positive sodium ions (Na+, atoms of sodium with a + electric charge) out of the cell, leaving behind negative ions, especially chloride ions (Cl-). The excess of negative ions left inside the cell makes it negative. The Na+ gets back into the cell when the cell is excited. (Na+ and Cl- are the atoms that form table salt. Dissolving table salt in water breaks it up into these two ions)