Commentators and practitioners often refer to the US controlled foreign corporation statute (or "CFC") as extremely complex and Byzantine in their construction and application. I would agree with this assessment to a point; if someone is simply trying to learn the pure mechanics of the statute then, yes, it is very difficult to fathom. However, when one looks at the rules after understanding the underlying policy for their implementation and overall effect, the statutory scheme becomes easier to comprehend. So, let's begin with an explanation of why the US (and other developed, OECD countries) put these types of rules into place.
To begin we will need to know a few definitions from section 7701. A domestic corporation is one "created or organized in the United States or under the law of the United States or of any State" while a foreign corporation is "one that is "is not domestic." Moving one step further, a foreign corporation is taxed by the US on income that is either connected with a "United States business" or is derived from sources within the United States. Putting all of these definitions together into a workable (and far more user friendly) statement, the US taxes a foreign corporation when that corporation either formally engages in a trade or business within US borders or derives some type of profit from an activity within the US. While this all may seem a bit obvious, knowledge of these definitions is key to understanding why the US implemented CFC rules.
Next, it's important to remember the US taxes US corporations and individuals on world wide income (income from "whatever source derived"). But given the above definitions, it would be possible for a US person to transfer his assets to a foreign company thereby removing the income from the US taxation, as that company would have no taxing nexus with the US -- they were not conducting a trade or business within the US or engaging in any non-business related transaction. And as the entity was not a partnership, the income would not pass through to the individual. And this is exactly what was happening to a larger extent in the 1950s -- US corporations and individuals would form foreign corporations outside the US' taxing jurisdiction while still living and residing in the US. This creates a "free rider" problem: people or companies who live/reside in the US receive all the benefits of taxpayer funded programs (the interstate system, public education, a judiciary to name a few) without funding them through taxes. And it is that behavior which the CFC rules were designed to prevent.
In general, the CFC rules attribute offshore corporate income to US shareholders when the perceived purpose of the offshore corporation is not to engage in legitimate foreign business (such as opening a "bricks and mortar" branch to sell products) but instead to divert income to a low-tax jurisdiction with the sole intent of removing it from the US tax base. As we move forward into a general overview of the CFC mechanics, keep this concept in mind as it helps to clarify the underlying CFC policy and makes the overall rules that much easier to understand.