Say, if your dns-servers are ns1.a.com and ns2.a.com, with their old ips glued at the registrar you registered a.com with.
Someone else, perhaps a reseller or something, has ns1.b.com and ns2.b.com, with the same ips as yours, basically making them look the same, but still "their own" so to say. I usually set this up for my resellers.
The reseller (or whatever) has the same ips glued with their registrar, so when you change yours at your registrar, they need to change theirs too, to point to the new ips. That is, if they point their domain, b.com, to ns1.b.com and ns2.b.com.
If you have a normal customer that simply points their domain at ns1.a.com and ns2.a.com, you dont have to do anything there. This also goes for resellers that point directly to ns1.a.com and ns2.a.com.
Now that didn't come out as simple as i wanted it to... but see if you can make sense of it