Electrical current results when a voltage or electromagnetic force causes movement of electrons. Since electrons need not be bound to atoms, it is important to exclude atoms, conductors, resistors, what have you in our definition of current flow.
Electrons in, electrons out
The most common mention of current flow concerns the movement of electrons within conductors to supply power to some kind of electrical load. A flow of positive charge gives the same electric current as an opposite flow of negative charge. Thus, opposite flows of opposite charges contribute to a single electric current. For this reason, the polarity of the flowing charges can usually be ignored during measurements. All the flowing charges are assumed to have positive polarity, and this flow is called conventional current. Conventional current represents the net effect of the current flow, without regard to the sign of the charge of the objects carrying the current.
In solid metals such as wires, the positive charge carriers are immobile, and only the negatively charged electrons flow. Because the electron carries negative charge, the electron motion in a metal is in the direction opposite to that of conventional (or electric) current.
An electrical or electronic load is something that needs electrical power to operate and uses more than it produces.
We have to drop into physics lecture mode for a moment. Temperature is a measure of the energy contained within a substance. Imagine for a moment that you used the Star Trek transporter to take one tiny atom out of a block of granite. That tiny atom was just in the process of bouncing around against its neighbors. It is now liberated. Imagine that it was liberated into a gravityless vacuum. If you were to slow that atom down to a standstill, you would have to add a quantity of energy to it. Right?
Now, imagine doing that for every last single solitary atom contained within that block of granite. You don't care which direction each atom is going; you just care how much energy it would take to stop each dead in its tracks. Got the picture?
Okay, so now we add all of that energy up. All of that THERMAL energy. In other words, thermal energy is the sum total of all the vibrational energy contained in the object's component parts. We could go on and discuss thermal conductivity, BTUs, calories, and their relationship to temperature but that would be too serious a digression.
Electron flow excitement
So, when electrons flow through a material, they cause anything from an insignificant quantity to a catastrophic amount of vibrational energy or heat to be created.
Insulators do not normally allow electron flow. To overcome that effect, voltage would have to be raised tremendously high. For a spark to cross the insulating gap of air between his finger and the office door, the cube farmer would have to build up thousands of volts of static potential. However, there is only the air there to be heated and so it simply has too few bits of matter to support heating. Vacuum, as you already surmised, has only the electrons themselves and only during the course of their passage.
Semiconductors will begin conducting after only a little voltage 'encourages' the flow. Before, it acts like an insulator. After, it acts like a conductor.
Resistors are designed to resist the flow of electrons. They may be of many materials and, in fact, even conductors display the same characteristics, but to a far smaller extent. Resistors are manufactured as identified components in circuitry. Not surprisingly, the filaments in electric lights, electric stove coils, blow dryer elements and space heater coils are also resistors.
Conductors allow electrons to flow quite freely. They do, however, present some resistance to current flow. Thus, you can cause them to heat up by 1) passing more than the designed current or 2) insulating them so that the tiny heat that is normally generated has nowhere to go and builds up to a potentially disastrous temperature.
Superconductors are conductors with the characteristic of passing electrons with negligible heating and resistance. The current state of technology insists that they be cooled to a very low temperature. Should room temperature superconductors ever be created, there would be no power wasted over the (currently resistive) power lines between our power plants, and our cities and towns. That would cut carbon emissions, well, a whole lot.
Hot and hotter
In a lightbulb, that heat becomes so great that the tungsten filament glows white hot. Stove and blow dryer elements can glow red-hot. A space heater may not glow but it can still burn the dickens out of you if you are not careful. Light generated is directly related to temperature. If two objects give off the same color of light, they share identical temperatures.
Heat, so desirable in a light bulb, can be disastrous in your house wiring or your PC.
Experimentation in current carriers
Experimentation is used to determine a substance's resistance characteristics with regard to current flow. Experimental results show that increasing the conductor size decreases its resistance proportionately. So, double the cross-section of a wire and you halve its resistance.
The unit of current is the Ampere or Amp for short. It is defined as a specific number of electrons flowing across a specific point per unit time.
Current, Power and mathematic equations
We have spent a great deal of time talking about current and its thermal effects. Let's consider what we know. When voltage goes up in a circuit, current goes up. If I double the voltage and the resistance remains constant, I double the current. I also double the vibrations I'm causing so I double the amount of heat I am adding. In other words, doubling voltage doubles the power generated in the form of heat. This leads us to an equation. Power equals Current times Voltage. The symbol for Power is P, the symbol for Current is I, and the symbol for voltage is E. We have P = I * E.
As I double the resistance, I halve the current when constant voltage is applied. Resistance and current are inversely related. As I double the voltage, the current doubles as well. In point of fact, Voltage equals Current times Resistance or E = I * R.