NAP - Network Access Points

In the early days of Internet, there was a Network Access Point that provides a peer-to-peer connection between different ISPs. It was a kind of public network exchange facility that determines how traffic is routed.

NAP - Network Access Protection

The Network Access Protection is an access based protection that Microsoft started with its Windows Server 2008 operating system. The platform provides a way to evaluate the health of a host device attempting to connect to a network, and restricts the access if the requirements aren't met.

In terms of sleeping, "nap" is not a full form but a Noun. It is used to explain a brief period of sleep taken, especially during daytime.