As a verb, it means to shelter the people with welfare benefits to the point where they become incapable of contributing to society. The term is used pejoratively, often by those arguing against social welfare programs.
As a noun, it can be used for those who are pampered, sheltered, and weak. It often has a gendered connotation, implying that someone who is a mollycoddle is effeminate.
The term was coined by Theodore Roosevelt, who used it to describe colleagues he saw as weak.
Kevin P. Murphy explains: “Roosevelt asserted that colleges should never ‘turn out mollycoddles instead of vigorous men,’ and cautioned that ‘the weakling and the coward are out of place in a strong and free community.’ A paradigm of ineffectuality and weakness, the mollycoddle was ‘all inner life,’ whereas his opposite, the ‘red blood,’ was a man of action.”