The Constitution is indeed a flexible document. One reason the Constitution is flexible is because the language of many clauses in the Constitution is vague, perhaps deliberately so. This has led to a number of different interpretations in which a single clause is used to support different acts of government. For example, the Commerce Clause of the Constitution, (Article I, Section VIII, Clause 3) grants to Congress the power to
...regulate commerce with foreign nations, and among the several states, and with the Indian tribes.
Notably, the Constitution does not spell out exactly what regulating commerce, especially interstate commerce, actually entails. Consequently, the Clause has been used to support a wide variety of legislation, including regulating monopolies, prohibiting discrimination, and most recently (though the Supreme Court rejected this particular justification) the Affordable Healthcare Act. This has also allowed it to change as technology has altered the nature of interstate commerce. Another example is the Necessary and Proper, or "elastic" clause, which has been interpreted very broadly almost since the ratification of the document.
Many might argue that the Constitution is flexible because it contains provisions for amendment as well. While the amendment process does require a great deal of political consensus, making frivolous or contentious amendments unlikely, it does enable the document to change according to the times. So in these two senses, the Constitution is a flexible document.