To allow donors the option to dedicate their donation in honor or in memory of someone, follow these steps:
Log into your Org account, go to the campaign you wish to enable this feature for, and click Edit form on the right to edit the campaign.
Under the Custom Fields tab, toggle the option Donation in honor of & in memory of.
Select the options and features you wish to have.
Click Update & Preview, and you're done! Your donors are now able to dedicate their donation in honor or memory of someone.
For an example of an organization that enables this feature, take a look at The Halo Trust's donation page.