A NameServer is a server that translates Domain Names into IP Addresses. In other words, it's what allows you to enter www.example.com instead of 192.12.345.67 into your browser.
A great analogy is to think of a Nameserver as a Phonebook. Instead of entering phone numbers you enter contact names to make calls.
If you need to update your NameServers, it can take up to 48 hours for providers across the globe to update their DNS caches so that everyone can see your website. They're not being lazy, this is just the way the internet works.