Re: What is NT Authority?
"Local Service Account
The Local Service account is a built-in account that has the same level of access to resources and objects as members of the Users group. This limited access helps safeguard the system if individual services or processes are compromised. Services that run as the Local Service account access network resources as a null session without credentials. Be aware that the Local Service account is not supported for the SQL Server or SQL Server Agent services. The actual name of the account is "NT AUTHORITY\Local Service account"."
The Network Service is essentially the same thing but for networking aspects of your machine. The way I understand it, they are local accounts that run background processes but keep your machine more safe should something be compromised.
Hope that helps.