A friend asked me to introduce electronic components in a simple way, not teaching electronics in depth, but giving just enough information to “play”.
This makes sense: with a standalone Arduino board , You can make the onboard Led on pin13 blink, but not very much else.
With this post I try to summarize concepts, with a language understandable even to people that do not have a strong technical background. If You are interested in a more detailed technical explanation, this is not the right place, but google is always Your best friend 
All following formulas and concepts are valid for DC and may not be valid for AC
To follow this simple lesson on resistors You must be familiar with concepts like voltage and current. If not we can say, simplifying a lot (purists forgive me!), that given two points:
- voltage (V) is the measure of the strength electric charges are attracted between the two points
- current (I) is the measure of how many electric charges are moving per unit time between the two points.
The electrical resistance (R) is a measure of the opposition to the passage of the current through an element. Some materials offer a linear relationship between resistance, voltage and current; this relationship is expressed by the Ohm’s Law
1) 
The unit of measure of V is Volt, of I is Ampere and R Ohm or Ω
Resistor Symbol
A resistor is an electronic device that has as it’s primary function to offer electrical resistance following the Ohm’s law.
Under normal conditions we can consider the electrical resistance of a resistor a constant so, reading between the lines, we can infer from Ohm’s law that changing the voltage between the resistor terminals the current changes proportionally with a coefficient 1/R,
2) 
that means the bigger the resistance the smaller the current, the bigger the voltage the bigger the current.
An important parameter is the power (P) dissipated by a resistor; as a consequence of the opposition to the passage of the electrical current heat is produced. It’s very important to know how much power a resistor dissipates because overheating may lead to resistor failure.
3) 
The unit of measure of P is Watt
Substituing from 1) 
into 3) we obtain:
The meaning is that the bigger the voltage the bigger (squared !) the power, the bigger the resistance the smaller the power.
Notice that small variation of the voltage may lead to big changes in the power dissipated by the resistor.
Resistors manufacturers produce many types of resitors with different materials and standard power dissipation values ranging from 1/8W (125mW) to several Watts.
Most widespread resistors between hobbyists are made from carbon with a power dissipation of 1/4W (250mW), and look like small plastic cilinders with two metal terminals with 4 or more colored stripes. The color code gives information about the value in Ohm of the resistor and other parameters like tolerance and temperature coefficient.
If the resistor has 4 stripes the first and the second are the first and the second digit, the third the number of trailing zeroes the fourth the tolerance. For example Blue-Gray-Orange-Silver evals to 6-8-000-10% or 68000Ω 10% or 68KΩ 10%
Precision resistors have 5 stripes the first the second and the third are digits, the fourth the multiplier, the fifth the tolerance. For example Blue-Gray-Yellow-Orange-Red evals to 6-8-4-1K-2% or 684000Ω 2% or 684KΩ 2%.
If a sixth stripe exists it gives the temperature coefficient that means how many parts per million the resistor value changes for the variation of 1°C.
Resistors have a positive temperature coefficient that means that if temperature raises resistance increases.
The tolerance is how much the value of the resistor can differ from its nominal value; for example with 1KΩ 10% we can measure a value of 900Ω or 1100Ω
Resistors values were standardized by EIA (Electronic Industries Association) and assume quantized values depending on the tolerance. Most used resistors are of the series E12 corresponding to 10% tolerance (that means that between two decades there are 12 values. e.g. between 100 and 1000 we have 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820).
Resistors can be connected together in series or in parallel. Calculating the final resistance value is easy:
For example suppose R1=100Ω , R2=200Ω
Series Value R1+R2=100 + 200=300Ω
Parallel Value 1/(1/R1+1/R2)=1(1/100 + 1/200)=2000/300=66,7Ω
Parallelizing resistors is a good idea to increase power dissipation. Suppose You need a R of 250Ω 1W, You may make a parallel of 4 x 1KΩ 1/4W. This is because each resistor can dissipate 1/4W so 1/4W x 4 = 1W
Is always a good idea choosing a a resistor with a bigger power dissipation than requested, because this will prevent failure of the resistor over the time.