It's a good question, but there's no clear answer - it's been debated almost since it was written. The arguments can be broken down into two camps (all quotes from Wikipedia):
James Madison advocated for the ratification of the Constitution in The Federalist and at the Virginia ratifying convention upon a narrow construction of the clause, asserting that spending must be at least tangentially tied to one of the other specifically enumerated powers, such as regulating interstate or foreign commerce, or providing for the military, as the General Welfare Clause is not a specific grant of power, but a statement of purpose qualifying the power to tax.
Alexander Hamilton, only after the Constitution had been ratified, argued for a broad interpretation which viewed spending as an enumerated power Congress could exercise independently to benefit the general welfare, such as to assist national needs in agriculture or education, provided that the spending is general in nature and does not favor any specific section of the country over any other.
Up until 1936, the Madison viewpoint was the predominant one, but since then, case law has sided more and more towards the Hamiltonian. This is despite the fact that Madison was more involved in actually writing the clause, and is more likely to be an authoritative source on the original intent.
Proponents of the Madisonian view also point to Hamilton's limited participation in the Constitutional Convention, particularly during the time frame in which this clause was crafted, as further evidence of his lack of constructive authority.
In 1936, in United States v. Butler, the supreme court held that
[T]he [General Welfare] clause confers a power separate and distinct from those later enumerated, is not restricted in meaning by the grant of them, and Congress consequently has a substantive power to tax and to appropriate, limited only by the requirement that it shall be exercised to provide for the general welfare of the United States.
It later revisited and expanded on this decision in discussing Social Security (1935) and whether the government could withhold funds from states (1987). In summary, so long as the money gathered from taxes is being spent for "the general welfare" (however Congress defines it), then Congress is permitted to impose the tax.
In short, originally it was (probably) intended narrowly, but it has since been interpreted broadly by the courts.