Fundamentally, it is a difference between how the electrical energy moves through the wires of a circuit. Simply said, DC, or Direct Current, moves in one direction through the wires, from point A to point B. On the other hand, AC, or Alternating Current, moves back and forth between points A and B.
DC Electricity is the kind of electricity used in cars - like the 12 volt battery in your car. AC electricity is the kind of electricity used in the home, sometimes known as "household electricity". AC electricity is what comes out of the wall outlet where you plug in a blender or a TV.
To help understand how DC electricity works, imagine a simple circuit described in the following way: starting at a battery (like a 12 volt car battery), a wire running from the Positive Post (point A) to a light bulb, and back to the Negative Post (point B). When you touch the wire to the Negative Post, the light goes on. The energy is moving from the Positive Post, all the way down the wire to the bulb, through the light bulb, and back to the Negative Post. When it moves through the light bulb, it creates heat, and light.
Electricity can also be thought of like water. If the wire was a tube, and the energy were water, it would be flowing all the way through the tube - from the positive, through the light, to the negative. This continuous flow of energy, in one direction from point A to point B, is DC (Direct Current) electricity.
Now, to understand AC electricity, imagine if you were to replace the battery in the previous example, with a grounded wall outlet. A grounded wall outlet does not have Positive and Negative. Instead, it has three sockets - one round hole, which is called "ground", one small slot, which is called "hot", and one large slot, which is called "neutral". The "ground" socket is a safety device, to provide an alternate route for the electricity to go "back to ground" in case there is a short in your blender. This way, the electricity goes to ground rather than through your body.
With AC electricity, the energy is "pushed" from the "hot" side of the outlet - but instead of being pushed all the way through the wire, it is pushed and pulled back and forth through the wire. The wire going to the light bulb and back is the same as in the DC example above, however instead of Positive and Negative, one end of the wire would be connected to "hot" (point A) and the other to "neutral" (point B), and the energy moves back and forth through the wire in between. If the wire were again to be considered a tube, it would be full of water, and the water would be moving back and forth through the tube. AC or "Alternating Current" means oscillation back and forth, at some frequency of oscillation. Typically in America the frequency of AC electricity is 60 Hz, or 60 oscillation's per second. This means the energy is moving back and forth (switching direction) at a rate of 60 times per second.
Why do we have two different types of electricity? In short, it's because AC electricity travels over long distances much more efficiently than DC electricity. So when you consider the many hundreds or thousands of miles the electricity travels from the power plant to your home, it becomes much more cost effective, and efficient, to transmit the energy as AC electricity rather than DC. Also, AC electricity is a little safer than DC, in case someone accidentally gets shocked.
Why would either AC or DC electricity cause the light bulb to go on? Imagine it like this: if the electricity is thought of as water, the light bulb may be thought of as a "bottleneck" in the tube. The bottleneck is smaller, so at this point there is more friction - or a resistance to the flow of energy - through that point. As you might know, when there is resistance, there is heat - and if there is enough heat, it will radiate - as a light. Think of a hot iron that's so incredibly hot that it glows red - first it gets hot, then it glows!
So the energy flowing through the bottleneck of the light bulb first produces heat, and then light. Now, the bottleneck doesn't care whether the energy flows continuously in one direction, as in Direct Current, or if it changes direction back and forth, as in Alternating Current. Either way, the energy is still moving through the bottleneck. All that matters to a bottleneck is the energy moving through it, so it can produce heat, and then light.
AC and DC electricity - household Alternating Current, and automotive type Direct Current. Two different ways of using the same electrical energy.