Custom domain feature allow you to use your domain or subdomain for all external links for Projects and Events.
So instead youengage.me/p/project_code you can setup links for Projects to be like yourdomain.com/p/project_code or yourdomain/e/event_code for Events.
Of course, there is also an option to setup not only top-level domains but also subdomains so it can be for example forms.yourdomain.com/p/project_code.
This feature is available in our Business plan and you can setup this in account settings
To setup your custom domain you need to have access to your domain DNS settings and create CNAME or A entry ( depend if you want to use top-level domain or subdomain ) and also TXT record.