When a
company pays
dividends, in some countries it can choose whether to pay
company tax on those dividends or not. If it chooses not to pay tax on them, it doesn't mean that the company's bypassed the tax system, it just means that whoever received the dividends has to pay it.
If it does choose to pay tax, then the dividends are considered "franked" (not surprisingly, shares that have not had tax paid on them are considered "unfranked"). This makes a difference when it comes to doing one's personal tax return. If the shares are franked, then the amount of tax that was paid on them is credited to you as tax paid, even though the amount of tax you pay and the company pays are very different. If they're unfranked, you have to pay tax on all of the dividends. This can be a very nasty surprise come tax-time.