Name servers tell the Internet how to find you.  When you edit the name servers in your domain record, you are telling the Internet which name server provides the most up-to-date directions.  If you don't change the name servers in your domain record (let's say you use your old web host's DNS), then your web site will point to a server that isn't hosting your domain.  Or, if the old web host deleted you from their DNS, your domain wouldn't work at all.