In summary:
Charitable contributions or donations can help US taxpayers to lower their taxable income via a tax deduction.
To claim a tax-deductible donation, you must itemize on your taxes.
Your donation must meet certain guidelines to qualify - for example donating to a qualified organization.
The amount of charitable donations you can deduct may range from 20% to 60% of your AGI
For UK tax benefits on donations, please see What is Gift Aid?