Nameservers tell the internet which company is responsible for managing where your domain points - your email, your website, everything.
When someone registers a domain, it's initially pointed at the registrar's default nameservers. To connect the domain to your actual hosting account, you (or your host) update the nameservers to point at your hosting provider's nameservers instead - usually something like ns1.yourhost.co.za and ns2.yourhost.co.za.
Once that change is made and has propagated (see our article on DNS propagation), your hosting provider takes over control of where your website, email and other domain-based services point.
If your website or email suddenly stops working after a provider switch, incorrect nameservers are one of the most common causes - it's always worth double-checking these first.