Gift Aid is a tax efficient method for individuals to make donations to charities. A Gift Aid donation from an individual is assumed to be paid net of basic rate income tax. The charity can reclaim this tax from HMRC provided the donor has paid an equivalent amount of UK income tax and/or capital gains tax. So assuming the donation is valid, HMRC will top it up by 25%, and for every £100 a basic-rate taxpayer donates, the charity receives £125.
There are additional reliefs available for higher and additional rate taxpayers via self-assessment tax returns or other contact with HMRC.