BigH is correct. Get a copy of ASTM D698 (Standard Proctor) and ASTM D1557 (Modified Proctor) and read them. The Proctor method, commonly used, was developed by R.R. Proctor in 1933.
The two values in each example you gave are the following:
12% @ 100 pcf ..... (Generally is written as 100pcf at 12%).....the 100 pcf is the maximum dry density as determined by the laboratory test. Since you asked about the modified Proctor, we'll presume that those values you gave are from a laboratory test using the modified Proctor method (ASTM D1557). The 12% is the optimum moisture content. These are determined from the peak of the laboratory curve.
These numbers are developed through the laboratory test. For most tests, 4 specimens of the same soil are compacted in volumetric molds with a known/calibrated volume. The test procedure starts with a dry soil and the only variable throughout the test sequence is to vary the moisture content of each specimen. As an example, moisture is added to the dry soil to start with a moisture content of around 8 to 10 percent. For the modified Proctor, the specimen is compacted in 5 layers with 25 blows of a 10 lb rammer in each layer. This defines the input compaction energy to the specimen. Each specimen is compacted the same way, only varying the moisture content as noted. The next specimen then has moisture added before compacting in an increment of about 1.5 to 2 percent, so this specimen might have a moisture content of, say, 10 to 12 percent. The same procedure is used through the 4 specimens.
For ease of comparison, we use the dry unit weight of the soil, not the wet unit weight in plotting our results. From these results a plot can be developed of dry unit weight in pcf vs. moisture content in percent. This results in the "Proctor Curve" as we typically know it.
The laboratory test (Proctor) is then used as the basis of comparison to field density tests or in-place density tests done at the site to determine the percent compaction for specification compliance. As an example, suppose your field density test shows that you have an in-place wet density of 103.6 pcf and a moisture content of 10.7 percent. The dry density of the soil in place is 103.6 /(1+moisture content) or 103.6/(1+0.107)=93.6 pcf. If you compare this to your example of 100 pcf @ 12%, then you have an in-place compaction of 93.6 or 94 percent.....just under a typical 95% compaction requirement. This tells you that you need to compact more.
We could go on and on about this concept. I am attaching a short summary of "How to Use a Proctor Curve". This is similar to the same concept found in the textbook "Principles and Practices of Commercial Construction", 9th Edition, Pearson Publishing.
