In simple terms, a domestic company is an orgnisation that is incorporated in and conducts its affairs in its home country. They are registered and liable to follow all the rules and regulation of the country where they are registered.
As per Section 2(22A) of the Income Tax Act, 1961, “domestic company” means an Indian company, or any other company which, in respect of its income liable to tax under this Act, has made the prescribed arrangements for the declaration and payment, within India, of the dividends (including dividends on preference shares) payable out of such income.
Domestic companies registered in India are taxed differently than a non-domestic business.
Link to see income-tax rates applicable in case of domestic companies.