Why are DAFs gaining in popularity compared to direct donations to charities and foundations?
This IRS article generally explains the rules covering income tax deductions for charitable contributions by individuals. You can find a more comprehensive discussion of these rules in Publication 526, Charitable Contributions, and Publication 561, Determining the Value of Donated Property.
Using charitable trusts, people can turn appreciated property (property that has gone up significantly in value since it was acquired) into income-generating investments without paying capital gains taxes on the profits. In addition to helping a good cause, donors can receive additional tax benefits.