A resident is a taxpayer with unlimited tax liability.
It is an individual who has a permanent residence in a given country, has a family there and resides in the country at least 183 days in a year. People who go to work abroad, but have permanent residence and a family in their home country are not residents. In this case they fulfil only one condition of residency: living abroad over half a year.
If someone is a resident of another country that means that his worldwide income is taxed there (home country income + income from abroad)
Yes, tax residency can be chosen if you fulfil the conditions of both your home country and foreign country. However the tax office usually insists on only people with permanent residence in their country being residents.
The main benefits of residency are tax deductions, tax reliefs and tax bases. For example a resident in Slovakia pays a 19% tax, in Czech republic it is 15% and in Austria based on income it can be between 0% to 55%.
The amount of tax paid and tax reliefs are higher in some countries.
In every country you document your residency status by filing a tax return. The tax return bases its calculation on various documents depending on the country. Here are some examples: