If you make a donation through the FirstGiving Donate Button on a nonprofit's website, you have the choice of marking it in honor or in memory of someone. If you do that, you'll be asked for the email and mailing address of the person you would like to notify about this donation (for instance, a family member of the person in whose memory you are donating).
They will receive a notification that looks like this:
[Your Name] has made a donation to [Name of Nonprofit].
[Message from the nonprofit, if they have written one]
Thank you for your donation,
The FirstGiving.com Team