The advantages of a LAN are the same as those for any group of devices networked together. The devices can use a single Internet connection, share files with one another, print to shared printers, and be accessed and even controlled by one another.
LANs were developed in the 1960s for use by colleges, universities, and research facilities (such as NASA), primarily to connect computers to other computers. It wasn't until the development of Ethernet technology (1973, at Xerox PARC), its commercialization (1980), and its standardization (1983) that LANs started to be used widely.
While the benefits of having devices connected to a network have always been well understood, it wasn't until the wide deployment of Wi-Fi technology that LANs became commonplace in nearly every type of environment. Today, not only do businesses and schools use LANs, but also restaurants, coffee shops, stores, and homes.
Wireless connectivity has also greatly expanded the types of devices that can be connected to a LAN. Now, nearly everything imaginable can be "connected," from PCs, printers, and phones to smart TVs, stereos, speakers, lighting, thermostats, window shades, door locks, security cameras--and even coffeemakers, refrigerators, and toys.
