Entrepreneurs managed to create large-scale corporate enterprises in the late nineteenth century by using questionable methods to drive their competitors out of business.

At that time, during the so-called Gilded Age, business regulation was virtually nonexistent. As a consequence, wealthy entrepreneurs—known pejoratively as robber barons—were able to use all kinds of sharp practices to increase their wealth and power at the expense of the competition.

Captains of industry like John D. Rockefeller used their extraordinary wealth and power to buy up smaller companies, ensuring that they had no serious competition and could make even bigger profits.

Once such entrepreneurs had driven their competitors out of business, by fair means or foul, they were able to create large-scale corporate enterprises that virtually cornered the market in a variety of industries, most notably steel, oil, and railroads.

The so-called robber barons, following Rockefeller's example, also used novel business arrangements called trusts that involved the combination of the main company—which, in Rockefeller's, case meant Standard Oil—with affiliated companies in order to create a giant corporate entity that would monopolize the provision of the relevant product or service.

What explains the large-scale enterprises of the late nineteenth century?

So are you just asking why businesses got to be so big in the late 1800s?  If so, the main reason is technology.

Before the civil War, especially, it was very difficult to make a really large business.  There were not that many large machines that could produce goods on a large scale.  Even if there had been, there were not any huge markets, tied together by railroads, that could consume all the goods.  The lack of railroads also made it much harder for factories in one area to get raw materials from another area.  It was much more necessary to have smaller factories spread around the country.

As the 1800s went along, the boom in railroad tied markets together much more efficiently.  Along with this came technological improvements that made larger machines possible.  In addition, things like the telegraph made communications between parts of a large company much more possible.

Because of all these technological changes, large scale enterprise became much more prevalent in the late 1800s.