WINS is an implementation of the NetBIOS P-node server. What this means is that Windows PCs can find each other on the network by registering themselves with a centralized server, then asking that server about other PCs. Contrast with NetBIOS
NetBIOS was developed in the mid-1980s by IBM, Sytek, and Microsoft. Its purpose was to allow PCs to communicate over a local area network, especially IBM's 3mbps Ethernet-like cable service as well as IBM's later Token Ring LANs.
It allows NetBIOS-aware applications to communicate regardless of the underlying infrastructure. For example, on the older Windows PCs, you have the choice of installing NetBEUI (NetBIOS raw over Ethernet) or NetBIOS over Novell's IPX. Yet another option is NetBIOS over TCP/IP.
WINS is just a component of the NetBIOS over TCP/IP implementation. It is not used with NetBIOS over any other transport.
Contrast with DNS
WINS is similar to DNS: both systems will resolve a name into an IP address. DNS solves the general Internet naming problem, WINS is designed only for NetBIOS names. It is only used in the cases where NetBIOS applications (such as Windows File and Print Services) need to talk to each other.
However, Microsoft makes "helper" services. If you need a DNS name but one cannot be found, Windows will lookup the name in the WINS server. Similarly, if a NetBIOS name cannot be found in the WINS server, Windows will attempt to lookup the name in the DNS server. This means that while WINS and DNS have completely different heritages that know nothing of each other, they effectively become interchangeable.
WINS vs. no-WINS
WINS isn't necessary for all communication. NetBIOS has been designed around a "broadcast" mechanism. The default Windows behavior is to simply broadcast information on the local network. Installing a WINS server (and configuring the clients to use it) will reduce broadcast traffic. Also, since broadcasts do not travel across subnets, WINS may be the only way that two distant machines can find each other.