Federal law has required that campaign contributions be disclosed since the passage of the 1910 Federal Corrupt Practices Act. The general idea is that voters should know who is funding a candidate's campaign. That tends to provide a good indication of what the candidate really stands for.
But contributors like to hide their contributions, and Congress does like to allow groups to be able to hide donors if their primary purpose is not politics and they principally want to educate the general population about the issues surrounding the campaign.
This creates an opportunity for clever people to avoid disclosure by calling themselves social welfare organizations and filing paperwork to the IRS stating such. These are the two categories that matter:
- Wikipedia: 501(c)(4) organizations.
- Wikipedia: 501(c)(6) organizations.
The increased use of these types of organizations as vehicles for campaign spending has led to the increase of what is called "dark money" since it is hidden, unregulated and growing fast.
For more:
- Wikipedia: Dark Money.
- Open Secrets: Political Nonprofits (Dark Money).
- Charles Koch Denies Dark Money Donations.
- Mother Jones: Follow the Dark Money.
- Newsweek: As Dark Money Floods U.S. Elections, Regulators Turn a Blind Eye.