After-tax investment income that is distributed by one U.K. company to another. This income is often distributed in the form of dividends. The idea behind franked income is to prevent double taxation.
If Company A receives a franked dividend from Company B, Company A does not have to pay corporate tax on the dividend because Company B has done so already.

In other words, once the issuing company has paid corporate tax on the income being distributed, the tax payment is attributed also to the companies who receive the franked dividend.