one needs standard procedures so that different results can be compared and related by different people.
The standard Proctor compaction test was developed in the 1930's, as far as I know. The idea was to determining (in the laboratory) the maximum density of soil which can be achieved in engineering practice, using the compaction equipment available at that time. So, the 25 blows on 3 layers somewhat resemble the compaction procedure in situ.
Proctor was doing road development projects where he needed to estimate the practically possible density of soil, which is different from theoretical density. He tried to solve this through laboratory tests by using various moulds and compactors and different combinations of blows and lift thicknesses. In this process he settled with 25 blows and 3 lifts.
The original Proctor Compaction Test of 1933 used cylindrical mold 4 inches in diameter and 4.6 inches high, with a removable mold collar 2.5 inches high. The mold volume is 1/30th cubic foot
A 5.5 pound hammer, 2 inches in diameter, was pulled upward and allowed to free-fall 12 inches, onto the soil (5.5 ft-lbs per blow)
The soil was compacted in three lifts, with an average thickness of 1.33 inches/lift.
25 blows were exerted per lift, which equals 25 x 5.5 = 137.5 ft-lbs. The total input energy for the three lifts was 3 x 137.5 = 412.50 ft-lbs on a soil sample with a volume of 1/30th cubic foot. This equals 12,400 ft-lbs of compactive energy per cubic foot of soil
This energy simulates the field compactive effort closely and hence he settled for this. Read the enclosed document for more details on the development of this test.