For a non-profit organization to have charitable status under the law means that a donation to that organization results in the issue of a tax receipt - that is, a receipt that entitles the donor to a tax deduction.
Accordingly, organizations with such status fall under much closer scrutiny than those without it. This is reasonable because:
Effectively, citizens of that jurisdiction give up a right to tax some amount on the assumption that the organization acts in their own interests. In the United States there are also complex rules about whether charities are registered per state or federally, and where they can solicit for donations and how. See alleged Wikimedia corruption for some standing issues on this.
Sometimes the powers of charitable status are ab/used to reflect political biases, e.g. Greenpeace is charitable in some countries, not in others, and the difference usually depends on political forces in power in each country.