Double Taxation is where the same income is taxable in two different jurisdictions. For jurisdiction for which Hong Kong has entered into a Double Taxation Agreement (DTA) with, and where the individual resides in, or the company is incorporated in, Hong Kong, the income which are taxed by the Hong Kong government will not be taxed again.
Territorial Source Principle of Taxation in Hong Kong
Note that Hong Kong adopts a Territorial Source Principle of Taxation, which means only profits which arose in, or are derived from, Hong Kong are taxable in Hong Kong. This means that profits generated from overseas are not taxable in Hong Kong, but are most probably still taxable in the country where the profits originated from.
This means that for individuals that work in a different country but resides in Hong Kong, depending upon different countries' laws, may be required to pay income tax from both countries.
But a DTA usually resolves this and the individual will only be taxed based on its residency. How the country of residence is determined for the purpose of taxes is subject to each DTA.
For companies, this means that profits derived from activities involving the two countries will only be taxed by one country, or, in the case of apportionment, profits derived from one country will be taxed by that country. No profits will be taxed twice.
Which Countries are Included?
Each DTA is different and so you may have to check the laws of each country for which your profits are derived from. For example, the United Kingdom has guidelines to help you determine where you are the resident of for the purpose of dual-citizenship of an individual, and thus where you should pay taxes, and also policies in regards to companies. In the UK, you'd have to manually apply for these tax relief, it is not done automatically.