An organisation or institute dedicated to research and advocacy on a particular area of social, political or economic policy.
Whilst often claiming to be independent, a think tank need not be non-partisan, declared or otherwise, or unaffiliated to a political party.
Though usually not for profit, a think tank is not obliged to publish its accounts or the source of its funding, unless it is registered as a company or charity.
Examples of think tanks in the UK (via Wikipedia) are: CIVITAS, Demos, the Institute for Public Policy Research, Policy Exchange and Reform.
The think tank, Transparify, which monitors other think tanks, regularly rates and reports on how transparent they are. See, eg, How Transparent are Think Tanks about Who Funds Them 2016?