These types of business entities get their name from the fact that items of income and expense flow from the business onto the individual tax returns of the investors. So, the business does not pay any income tax, it's the responsibility of the investors. Examples of flow-through business entities are partnerships and S corporations.
A limited liability company (LLC) can also be taxed as a flow-through. It will depend on how many members the LLC has and the election made on Form 8832.
How The Flow-Through is Taxed
Let's say you own 35% of a partnership. At year end the partners' share of income is $2,000. 35% of $2,000 or $700 is reported as income and taxed on your Form 1040.

