"
what context does ""enlargement of government power"" belong here?
It does not belong. Progressives do not wish to enlarge government power for the sake of enlarging government power. Progressives believe that modern society needs government intervention to ensure fair play, e.g. government regulation, and to protect the citizens, e.g. universal health care. Beck believes these are fringe views, but I do not. TFD seems to believe that believing in Progressive values is fringe, but he would be on Beck's side with side with that.
""You have taken the quote out of context and the source is a high school textbook,""
It is from Brittanica, and here is the full quote:
Origins of progressivism
Never were superficial signs more deceiving. Actually, the United States already was in the first stages of what historians came to call the Progressive movement. Generally speaking, progressivism was the response of various groups to problems raised by the rapid industrialization and urbanization that followed the Civil War. These problems included the spread of slums and poverty; the exploitation of labour; the breakdown of democratic government in the cities and states caused by the emergence of political organizations, or machines, allied with business interests; and a rapid movement toward financial and industrial concentration. Many Americans feared that their historic traditions of responsible democratic government and free economic opportunity for all were being destroyed by gigantic combinations of economic and political power.

Actually there was not, either in the 1890s or later, any single Progressive movement. The numerous movements for reform on the local, state, and national levels were too diverse, and sometimes too mutually antagonistic, ever to coalesce into a national crusade. But they were generally motivated by common assumptions and goals—e.g., the repudiation of individualism and laissez-faire, concern for the underprivileged and downtrodden, the control of government by the rank and file, and the enlargement of governmental power in order to bring industry and finance under a measure of popular control.
This is very non-ambiguous
This is an article from Center for American Progress the biggest Progressive group in America, and in it it describes in detail the origins of the progressive movement and it's continuance today.
""What is progressivism?
Progressivism at its core is grounded in the idea of progress—moving beyond the status quo to more equal and just social conditions consistent with original American democratic principles such as freedom, equality, and the common good. Progressivism as an  intellectual movement emerged between 1890 and 1920 as a response to the multitude of problems associated with the industrialization of the U.S. economy—frequent economic depressions, political corruption, rising poverty, low wages, poor working conditions, tenement living, child labor, lack of collective bargaining power, unsafe consumer products, and the misuse of natural resources.
""As a philosophical tradition, progressivism in its most complete form developed as a “new liberalism” for a new century—updating the American liberal tradition from its Jeffersonian, small-government, republican roots best suited for the agrarian economy of the nation’s founding era to a more democratic and modern liberalism capable of checking rising corporate power. The original progressives argued that changes in the economy’s organization required a more complete understanding of human freedom, equality, and opportunity that Jefferson championed so persuasively. Progressives believed that formal legal freedom alone—the negative protections against government intrusions on personal liberty—were not enough to provide the effective freedom necessary for citizens to fulfill their human potential in an age of rising inequality, paltry wages, and labor abuses. Changed conditions demanded a changed defense of human liberty.""
With the rise of the contemporary progressive movement and the election of President Barack Obama in 2008, there is extensive public interest in better understanding the origins, values, and intellectual strands of progressivism. Who were the original progressive thinkers and activists? Where did their ideas come from and what motivated their beliefs and actions? What were their main goals for society and government? How did their ideas influence or diverge from alternative social doctrines? How do their ideas and beliefs relate to contemporary progressivism?
'''The new Progressive Tradition Series from the Center for American Progress traces the development of progressivism as a