R-value is the measure of a substance's resistance to heat flowing through it. This is commonly used in the building industry, where it is used to refer to the effectiveness of insulation. High R-values will keep the summer heat and the winter cold out, reducing the energy spent on heating and cooling.
This is the formula for calculating R-value used in most of the world. (If you are American you should read this, but you will actually use the formula given below.) It translates as 'Kelvin times square meters, divided by Watts'. The temperature in Kelvins, in this case, refers to the difference in temperature between one side of the material (with a heat source behind it), and the other side of the material (with no heat source). We use a cross sectional measure of the mass (hence m2 and not m3). So it essentially says that the r-value is equal to the temperature difference between the two sides of the material when the flow of heat is equal to one watt per square meter.
This is exactly the same thing as above, but Americans, being bullheaded mavericks, use completely different units of measurement. This formula is square feet times degrees Fahrenheit per BTU per hour. (The Watts used above include the 'per hour' measurement by definition). Wikipedia gives these values for translating between the competing formulas: 1 ft²·°F·h/Btu ≈ 0.1761 K·m²/W, and 1 K·m²/W ≈ 5.67446 ft²·°F·h/Btu.
R-value is often written in shorthand as "R-20" ("an R-value of 20") R-value is the reciprocal of U-value, that is, R-value equals 1/U-value. U-value is therefor the measurement of heat flow, rather than resistance to heat flow. (U-value is often used for windows).
You may also hear the term K-value. If you haven't heard the term K-value, reading the following paragraph will just confuse you! Don't bother! So... if someone uses the phrase "K-value" they are referring to U-value as I defined it above, but they will also be using the phrase "U-value" in a different sense; they will use it to mean an average of heat flow for the entire structure, and will use K-value for only individual components of the structure. Because K-value isn't used very often, you will usually not have to worry about this.
R-value isn't necessarily the best way to measure a building's insulation, but it has become the standard unit of measure. This can be a major headache for anyone trying to convince building inspectors that it's okay to build using unusual materials. (Such as cob, adobe, straw, cordwood, tires, or rammed earth. And, it turns out, yurts are problematic too.) Many of these structures rely on high thermal mass to hold heat. Thermal mass doesn't resist heat flow; instead it soaks it up. This is often a much better solution. Yurts, on the other hand, often rely on a radiant barrier, that reflects heat rather than retarding its flow.
Here are some R-values of common material for reference (using the American system):
1/2 inch drywall: R-0.45
1/2 inch plywood sheathing: R-0.63
1 inch fiberglass batting: R-3.14 to R-4.30
1 inch Rock Wool Batting: R-3.14 to R-4.00
1 inch blown cellulose: R-3.13 to R-3.70
1 inch vermiculite: R-2.13
1 inch aerated concrete: R-1 to R-1.25
Dead air: ~R-1
These numbers are general, and may vary depending on brand. You can easily find the R-value of any given material when you buy it -- if it isn't stated on the packaging, just ask the vendor. Keep in mind that R-value may be stated per-inch or per-unit; it is assumed that you will not rip your batting to shreds and use it in little 1-inch pieces. Also, while the R-values stated on the packaging are what matter to your building inspector, keep in mind that they are not always 100% correct. Fiberglass batting has been found to give lower than stated R-values even when installed correctly.
Most R-values in this writeup come from http://www.coloradoenergy.org/procorner/stuff/r-values.htm