Pass-through taxation refers to the fact that a pass-through business pays no taxes. Instead, some control person pays the business's taxes through that person's own personal tax return.
Pass-through taxation typically applies to sole proprietorships, partnerships, and S-corporations, upon that entity's ability to prove that it deserves pass-through status. This is opposed to either traditional corporations or C-corporations, in which the company itself pays corporate taxes on income the corporation earns.
For more on pass-through taxation, see this National Law Review article: Impact on Individuals Operating a Business Directly or Indirectly through a Pass-Through Entity (McGinley and Lorch), this Southern Methodist University Law Review article: The Taxation of Private Business Enterprises (Yin), and this National Law Review article (Ashraf and Wallwork).