The primary purpose of a Local Area Network (LAN) can be understood by examining the definition and typical applications of LAN technology. A LAN is a network that connects computers and other devices within a limited area such as a home, school, computer laboratory, office building, or closely positioned group of buildings. It is designed to facilitate the sharing of resources, such as files, printers, games, or other services, within a smaller, localized environment.

Let's evaluate the provided options against this purpose:

1. To link wireless devices only:

   This is incorrect. While LANs can include wireless connections (Wi-Fi), they are not limited to wireless devices. LANs can connect both wired and wireless devices within a local area.

2. To connect social media accounts:

   This is incorrect. Social media accounts are accessed via the internet, which is broader than a local network. LANs do not specialize in connecting social media accounts.

3. To connect computers within a small geographical area:

   This is correct. As discussed, a LAN is specifically used for connecting computers and other network devices within a confined area, facilitating communication and resource sharing among them.

4. To connect global networks:

   This is incorrect. Connecting global networks is the role of Wide Area Networks (WANs), such as the internet. LANs are localized and cover much smaller geographical areas.

Therefore, the correct answer is: To connect computers within a small geographical area.

Conclusion: LANs are essential for creating a network among local devices, providing a platform for data exchange and resource sharing efficiently within a contained physical space.