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The primary function of a RADIUS server in network security is to manage remote access authentication. RADIUS, which stands for Remote Authentication Dial-In User Service, is a networking protocol that provides centralized authentication, authorization, and accounting management for users who connect to and use a network service.

When a user attempts to access a network resource, the RADIUS server verifies the user's credentials (like username and password) against a database. If the credentials are correct, the server grants access to the user; if not, access is denied. This centralized handling of authentication helps organizations ensure that only authorized users can access sensitive information and resources, which is critical for maintaining security in a network environment.

In contrast, other options do not align with the primary role of RADIUS servers. For instance, encrypting all traffic in transit is typically managed by protocols like IPsec or SSL/TLS, rather than RADIUS itself. Filtering incoming network connections is a function usually performed by firewalls, while detecting and blocking intrusions is the responsibility of Intrusion Detection Systems (IDS) or Intrusion Prevention Systems (IPS). Therefore, managing remote access authentication is the essential function that RADIUS servers provide, making it the correct answer.