The resolver ips are what is used for any dns lookups. It's most common to set them to your own server ip, or localhost (127.0.0.1). If you want to use external resolvers, then you have to get your datacenter's resolver ips, they may be different than their nameserver ips.
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A resolver is a server which does the actually lookups to nameservers. Different resolvers will result in slightly different IPs depending on their settings. DNS isn't monolithic and everyone using different resolvers is why you can't get a definite time for your DNS propagation when you update your domain's DNS. So while one set of resolvers may update ever 24 hours regardless of your zonefile's TTL, another set may follow it strictly and update every 3 minutes if you tell it to.