Child Nameservers are your own named private nameservers. These private or child nameservers can be created through the domain's current registrar.
These type of Nameservers are great for pointing your domain to your VPS, or simply looks better on WHOIS lookups. They are also widely used by Hosting Resellers.
ns1.exampledomain.com ns2.exampledomain.com ns3.exampledomain.com ns4.exampledomain.com
The exampledomain.com, in this case, would be your own Domain.
If your Domain was purchased through Hostinger - you are in luck, as you can setup your Child Nameservers with just a few clicks.
To setup your own Private Nameservers login to your Hostinger Profile and press on Domains at the top menu.
In there, locate the Child Nameservers menu. You can setup your own private nameservers there.