An international company is an organization that has business operations in several markets across the globe. The company may have its headquarters in one central location, but it has subsidiary offices in each of the countries it operates in.
There are many reasons why a company would choose to trade internationally apart from simple market expansion. International companies are able to take advantage of loopholes in local tax laws to transfer profits from one country to another and thus avoid paying tax or are taxed at a very low rate. This type of activity is perfectly legal, even though some people may think of it as a form of tax avoidance.