A Network Attached Storage (NAS) unit is a computer connected to a network that only provides file-based data storage services to other devices on the network. Although it may technically be possible to run other software on a NAS unit, it is not designed to be a general purpose server. For example, NAS units usually do not have a keyboard or display, and are controlled and configured over the network, often using a browser. 
A fully featured operating system is not needed on a NAS device, so often a stripped-down operating system is used. For example, FreeNAS, an open sourceNAS solution designed for commodity PC hardware, is implemented as a stripped-down version of FreeBSD. NAS systems contain one or more hard disks, often arranged into logical, redundant storage containers or RAID arrays. NAS removes the responsibility of file serving from other servers on the network. NAS uses file-based protocols such as NFS (popular on UNIX systems), SMB/CIFS (Server Message Block/Common Internet File System) (used with MS Windows systems), or AFP (used with Apple Macintosh computers). NAS units rarely limit clients to a single protocol.

NAS vs. DAS 

The key difference between direct-attached storage (DAS) and NAS is that DAS is simply an extension to an existing server and is not necessarily networked. NAS is designed as an easy and self-contained solution for sharing files over the network. 
Both DAS and NAS can potentially increase availability of data by using RAID or clustering. 
When both are served over the network, NAS could have better performance than DAS, because the NAS device can be tuned precisely for file serving which is less likely to happen on a server responsible for other processing. Both NAS and DAS can have various amount of cache memory, which greatly affects performance. When comparing use of NAS with use of local (non-networked) DAS, the performance of NAS depends mainly on the speed of and congestion on the network. 
NAS is generally not as customizable in terms of hardware (CPU, memory, storage components) or software (extensions, plug-ins, additional protocols) as a general-purpose server supplied with DAS. 

NAS vs. SAN 

NAS provides both storage and a file system. This is often contrasted with SAN (Storage Area Network), which provides only block-based storage and leaves file system concerns on the "client" side. SAN protocols are SCSI, Fibre Channel, iSCSI, ATA over Ethernet (AoE), or HyperSCSI. 
One way to loosely conceptualize the difference between a NAS and a SAN is that a NAS appears to the client OS (operating system) as a file server (the client can map network drives to shares on that server) whereas a disk available through a SAN still appears to the client OS as a disk, visible in disk and volume management utilities (along with client's local disks), and available to be formatted with a file system and mounted. 
Despite their differences, SAN and NAS are not mutually exclusive, and may be combined as a SAN-NAS hybrid, offering both file-level protocols (NAS) and block-level protocols (SAN) from the same system. An example of this is Openfiler, a free software product running on Linux-based systems.