Andrew Carnegie is best known for his work in the steel industry, but he was also one of the foremost philanthropists of his era. Carnegie spoke often about the evils of greed, and claimed that "...the man who dies thus rich dies disgraced" (Wikipedia). In other words, gaining wealth for its own sake is a useless endeavor, and it is incumbent on the wealthy to spend or give their money to worthwhile causes and people.
In his 1881 essay, "The Gospel of Wealth," Carnegie laid out his principles for philanthropic giving. The relevant part is this:
"These who would administer wisely must, indeed, be wise, for one of the serious obstacles to the improvement of our race is indiscriminate charity. It were better for mankind that the millions of the rich were thrown in to the sea than so spent as to encourage the slothful, the drunken, the unworthy. Of every thousand dollars spent in so called charity to-day, it is probable that $950 is unwisely spent; so spent, indeed as to produce the very evils which it proposes to mitigate or cure."
(Carnegie, "The Gospel of Wealth," swarthmore.edu)
His point is that charity for its own sake is a fine sentiment but a useless solution unless it is given to those who will use it to better themselves and their situations. By giving to those who then turn around and ask for more, and do nothing to help themselves out of their poverty -- or worse, to those who do not need it except to fulfill their own hedonism -- the giver enables a culture of failure. The receiving person should use charity to rise above the need for charity, instead of viewing it as an alternative lifestyle. In this sense, Carnegie echoes a statement made by Benjamin Franklin:
"I think the best way of doing good to the poor, is not making them easy in poverty, but leading or driving them out of it. In my youth I travelled much, and I observed in different countries, that the more public provisions were made for the poor, the less they provided for themselves, and of course became poorer. And, on the contrary, the less was done for them, the more they did for themselves, and became richer."
(Franklin, "On the Price..." 1776, historycarper.com)
Essentially, Carnegie is decrying those who make a lifestyle out of receiving charity for no further purpose, and those who enable them to continue doing so. The "worthy" man is one who will use charity to rise above it, and the "unworthy" man is one who will take and continue to take, with no thought of personal improvement.