Before the Tax Cuts and Jobs Act, U.S. companies and resident individuals could own foreign corporations that engaged in active trade or business activities, and pay significantly lower tax rates, as long as the income was not brought back to the U.S.
If a business was classified as an active trade or business, the corporate entity could be operated in a foreign tax jurisdiction with a zero or very low tax rate, and only pay the taxes that are due in that jurisdiction.
For example, in Ireland, the corporate tax rate is 12.5%, so a company could pay the lower rate and use the tax savings to invest back into the business. As a comparison, in 2017 the highest U.S. tax rate was 35% for corporations and 39.6% for individuals, so the tax savings used to be substantial.