The importance of the RADIUS shared secret and security:
Provides data integrity; meaning that you have confidence that the information received came from the trusted (by knowing the secret) source without modification.
Protects the user password during PAP authentication. Knowing the RADIUS shared secret, the clear-text password can be derived from the PAP encoded password.
Protects the RADIUS server from a variety of attacks by requiring all RADIUS data pass verification against the shared secret. Typically, this means the RADIUS server simply does not process the data, dropping the RADIUS requests.
Select strong shared secrets. Use one for each client, as much as possible. It is also recommended to have all RADIUS protected in a secure tunnel such as a VPN or RadSec.
For more information on RADIUS security, here are a variety of links: