As Jtsummers linked Wikipedia article explains, the term 'Think Tank' was originally applied to the RAND corporation, which was started by the Air Force in 1947 as an R&D organization within Douglas Aircraft, but soon became an independent company which was still largely funded by contracts from the US Department of Defense.

RAND was enormously influential in US and world politics and technology in the 1950s, 60s and 70s. People who worked at RAND included the nuclear strategist Herman Kahn, who wrote a horrifying book On Thermonuclear War and become one of the models for Dr. Strangelove (in that movie it's called the BLAND Corportation), Daniel Ellsberg, who leaked a copy of the Pentagon Papers secret history of the Vietnam War he found at RAND, and Paul Baran, who proposed a national packet switched computer network, which provided the technical foundations for the Arpanet and later the Internet.

The book The Wizards of Armageddon by Fred Kaplan tells the story of the early days at RAND.

http://www.fredkaplan.info/wizards.htm

Availble tech reports from RAND include some of Herman Kahn's early work:

https://www.rand.org/pubs/authors/k/kahn_herman.html

and Paul Baran's computer networking proposal, as well as some remarkably prescient essays on the social and political implications:

https://www.rand.org/pubs/authors/b/baran_paul.html

Reports like these (as well as the secret ones that are never released to the public) are the products of a think tank. Think tanks exist to produce these reports, and to support their authors and other spokespeople who publicize and advocate for them.

https://en.wikipedia.org/wiki/Think_tank

Generally speaking, a group who spends their time "thinking". They will often be posed with questions or scenarios and try to develop models and answers around that. Explore some policy concepts, the consequence of some technological development (or the absence of that development), etc. The more prominent ones that pop up in the news in the US are often focused on economic, domestic, or foreign policy areas, but that's not the only thing they work on.

They're the kinds of groups you may go to to ask, "What if we had a UBI of $20k (in 2022 dollars) for every US citizen (regardless of age)?" and they'd develop various models, policy proposals, and possibly experiments to be conducted to analyze it. They may be asked to do a post hoc analysis of some policy or action to determine efficacy (or inefficacy), and so on.