Like most subparts in the US tax code (the CFC rules are a sub-part to sub-chapter N in the code), the CFC rules have specific concepts and definitions that apply only to this particular sub-part. The most important definition is that of a "US shareholder." In addition, like most sections in the code, the CFC rules require us to reference multiple sections to get a complete definition.
Let's start with section 957, which states:
For purposes of this subpart, the term “controlled foreign corporation” means any foreign corporation if more than 50 percent of—
(1) the total combined voting power of all classes of stock of such corporation entitled to vote, or
(2) the total value of the stock of such corporation,
Remember that under the tax code's definitions section (section 7701), a "foreign" corporation is one not formed in the US. So, according to the CFC definition, a non-US company that is owned by a "US shareholder" is a CFC. This, of course, leads us to define a "US shareholder" which is defined in section 951(b):
For purposes of this subpart, the term “United States shareholder” means, with respect to any foreign corporation, a United States person (as defined in section 957 (c)) who owns (within the meaning of section 958 (a)), or is considered as owning by applying the rules of ownership of section 958 (b), 10 percent or more of the total combined voting power of all classes of stock entitled to vote of such foreign corporation.
And finally, attribution rules from section 318 apply under section 358, preventing a US resident from diversifying his ownership over several companies and or family members to theoretically prevent technical ownership while still actually remaining in control.
Putting these two sections together, we arrive at the following definition: if more than 50% of the combined voting power of a foreign (non-US company) is owned by a "US shareholder(s) (individuals who each own at least 10% of the stock)" we have a controlled foreign corporation, thereby requiring us to include certain types of income from that company in each shareholder's gross income on a pro-rata basis.
It's very important to note that we have two ownership thresholds to meet in this definition. First, we have to establish majority control by "US shareholders." This means that if the foreign corporation is majority owned by foreigners (non-US individuals), a CFC does not exist. In addition, we only have to include certain types of income in the personal gross income of US residents who own more than 10% of the company.
Next, we'll start to look at what types of income we need to include.