The idea that "great men" carry history forward is actually a bit older than the formalization of "The Great Man Theory" by Thomas Carlyle in 1840.

More specifically, various world leaders prior to 1840 (including ancient figures such as Hannibal and Caesar) are now recognized / theorized as having developed what is now termed a "cult of personality".

This is, in simple terms, the use of propaganda and good PR to create an idealized image of the leader. In practical terms this is a mechanism of social control that helps create popular support for a leader, particularly as the cult of personality tends to equate the said leader with the state as a whole. In historical terms it tends to skew the focus towards the said leaders and attribute actions to them (fairly or unfairly).

An example of attempts (deliberately or not) to create a cult of personality can be found in Caesar's authorship of the Commentaries on the Gallic War. While the book is highly lauded, it must be remembered that Caesar was becoming a figure of controversy among the Roman Senators and the book in large part justifies his actions and paints him in a distinctly heroic light. For instance he claims to have been in the thick of the fighting during the great siege at Alesia, and that his personal presence helped rally the wavering troops; thereby implying it was his greatness and force of charisma that won the battle. True or not, it confirms the rather sardonic observation of modern historian Robert Citino that no one ever writes a biography that is critical of their own self.

Reaction to the GMT however was positive in 1840, in large part due to the climate in Europe at the time. It was quite frankly the start of an imperialistic Europe that was about to impose its control over much of the rest of the world; and the Euro-centric roots of the theory meant that most of the exemplars of "Great Men" were European figures such as Napoleon. This fed into the climate of European exceptionalism which fuelled the age of imperial expansion.

Edit: Added an example of Caesar in the Gallic Wars.