The simple answer is that it is a matter of how taxes are filed in relation to sole proprietorship, compared with LLC, S Corp and C Corp. I've seen them discussed as having value there, and explained below a high level/rough overview why it those difference exist. I have never seen someone quantify it though. But it is about taxes, and claiming of expenses vs itemized deductions. 

So, the article makes an assumption about prior knowledge for the different entity types. 

An S Corp is a C Corp that is taxed like an LLC, because the tax profit or loss flows directly from the entity to the ownership. Which is why they are called "Flow through entities." A C Corp doesn't have this functionality. It is a completely separate entity and company tax filings are not connected in any way with ownership.

The place where this would be of benefit, is if as an owner of a C Corp, a salary is collected, which is a deductible expense for the corporation, but that salary is income on the personal return of the owner/employee. Which is fine, an S Corp can utilize this functionality and is a very common arrangement. But in a "Flow through entity" if the entity makes a profit distribution. There is no tax extra taxation, as the tax profit or loss has already flown through to the owner, but with a C Corp, that distribution will have been exposed to taxes through the C Corp, and also as profit received by the owner, which is "Double taxation."

The reason filing an entity can save money, whether LLC, S Corp, or C Corp can save money is on taxable expenses. Certain expenses are easier to write off as expenses to the entity than they are to a sole proprietorship. Because buying a couch in an office is an easy expense to claim because it is furniture in an office, and is accounted for with the entity on  a separate tax schedule before flowing down to the owner. When it is a sole proprietorship, there isn't a separate area, it would need to be claimed as itemized deductions and go directly onto the owners personal tax return. And there are a lot of restrictions on itemized deductions for personal returns.