(EU) (US) Invented by Georg Ohm in 1827, resistors are one of the most commonly used items in electronics. Simply put a resistors does what the name says, it resists the flow of electrical current.
For some indepth information check out, http://en.wikipedia.org/wiki/Resistor on wikipedia.
Definition
A Resistor is an electrical device that resists the flow of electrical current. It is a A passive device used to control, or impede the flow of, electric current in an electric circuit by providing resistance, thereby developing a drop in voltage across the device.
Overview
The resistance value is specified in ohms, the standard symbol is "R" or Ω. Resistor values are often stated as "k" (kilo, or times 1,000) or "M", (meg, or times 1,000,000) for convenience. There are a few conventions that are followed, and these can cause problems for the beginner. To explain  a resistor has a value of 2,200 Ohms.


Color Scheme
One key thing to note is that resistor values are always coded in ohms (Ω). The bands below are you key to what each one means. There is not always 4 of them (sometimes less) but to notice the gap on the 4th ribbon "D" in this example below.
 A :: The 1st significant figure (far left side)
 B :: The 2nd significant figure
 C :: The decimal multiplier
 D :: (* If present *) Tolerance value in percent. Note: no color means 20%
Ohm's Law
Resisters follow Ohm's law which states that the current through a conductor between two points is directly proportional to the potential difference across the two points. So what does this mean? Well lets show some math equations to further confuse you; just remember that V=voltage, I=current and R=resistance. There are other versions of Ohm's law, however on the macroscopic level our equations are more commonly used and simpler that those used by physicists.
When I was taught beginners electronics we first learned the Ohm's Law Triangle (see below) which can be easily interchanged through math.
It is a very simple concept.
How else can we calculate Ohm's Law? No worries we'll take all the guess work out of the way for you: