On Christmas Day 1780 Thomas Jefferson proclaimed that,
“We shall divert through our own Country a branch of commerce which the European States have thought worthy of the most important struggles and sacrifices, and in the event of peace [ending the American Revolution]...we shall form to the American union a barrier against the dangerous extension of the British Province of Canada and add to the Empire of liberty an extensive and fertile Country thereby converting dangerous Enemies into valuable friends.”
In this statement he laid out the principle foundations of a very important concept. That being one of the United States of America's responsibility to the largely (at that time and even today) 'unfree' world. A responsibility of promulgating freedom and liberty wherever the U.S. could. Ensuring people ran the countries in which they lived and determined their own lives and commerce and weren't being coerced by brutal despots.
Whilst this concept has been used to justify military intervention and imperial policies throughout American history -- the war in the Philippines in the early 1900's being the most striking and salient example – it is nonetheless a concept that lays out a vision of an internationalist America as opposed to a provincial one. As you know Jefferson's warning against America becoming involved in “entangling alliances” is often invoked by many American politicians who advocate more inward looking policies as opposed to more involvement when it comes to aiding those seeking to democratize their lands overseas.
Jefferson's contention that the United States should be an empire of liberty doesn't necessarily contradict his famous entangling alliances statement. Instead it rectifies a vision of an America which advocates, and on the grounds of principle supports the proponents and those fighting for, liberty around the world in order to garner peace and fair commerce with the nations and peoples of the world. Something which isn't feasible or possible when autocratic and kleptocratic elements the world over suppress large swaths of the worlds population in order to enrich and empower themselves through brute force and ultimately at the majority of the peoples expense.
During Jefferson's time as president he oversaw the Louisiana Land Purchase from Napoleons France in 1803. On that occasion of the doubling of the territorial size of the republic Mr. Jefferson said that, "I confess I look to this duplication of area for the extending of a government so free and economical as ours, as a great achievement to the mass of happiness which is to ensue."
Given the nature of democracies with limited government Jefferson even implied that he saw no real end to the expansion of such an empire of liberty. He once wrote that, "where this progress will stop no-one can say. Barbarism has, in the meantime, been receding before the stead step of amelioration; and will in time, I trust, disappear from earth."