Features of the Design
The reason this task has remained in use for so long is that it requires almost no knowledge. Items probing vocabulary or general knowledge turn differences in native language and schooling directly into differences in score, whereas changes in visual attributes such as form, count, orientation, and fill look the same to a speaker of any language. Items are arranged in graded order from easy to hard, and in the later stages several rules operate at once. The word progressive in the name refers to this construction of difficulty.
What It Captures
In the course of answering, the examinee repeatedly breaks a figure into its attributes to identify which element is changing, forms a hypothesis about the rule governing the change, and tests it against the next element. Because the hypotheses have to be held in mind throughout, working memory capacity bears on performance. What is being captured is the ability to grasp an unfamiliar rule on the spot - something close to fluid intelligence - which is a different property from the volume of knowledge accumulated. The correlation between performance on this task and on memory tasks is thought to come from the shared load of holding hypotheses.
Cautions When Taking a Simplified Version
Simplified versions on the web inherit the original's property of requiring a rule to be grasped on first sight without depending on knowledge, but they differ decisively in not being standardized. With no age-banded reference sample and no control over the testing environment or the number of retakes, the number produced cannot be interpreted as an intelligence quotient. Familiarity with a fixed format will raise the score, but that is fluency with the task. Using it to compare against your own earlier results taken under the same conditions, rather than against other people, fits what it can actually support.