In order to do that you need to create a CNAME or ALIAS record in Namecheap for the domain you own. Which record type you should create depends on the domain type you like to connect.
Subdomain (e.g. sub.domain.com): CNAME record
Enter your full subdomain as the host name and paste the DNS target you copied from Balloonary as the value.
Apex domain (e.g. domain.com): ALIAS record
Enter the ‘@’ symbol as the host name and paste the DNS target you copied from Balloonary as the value.
Please notice that it takes a bit of time until these settings are propagated and live, sometimes up to 48h.