Why is the star property important
This equation expresses a confidentiality property. There are two ways of looking at it: what does it permit and what does it prevent.


Prevented: writing secure information to an insecure place.
Permitted: writing insecure information to a secure place.


Clearly, the former is good, otherwise, for example, your PIN number (secure) could become accessible to untrusted third parties.

From a security perspective, the former is safe, because no secure information is leaked. It allows cases such as where you report your daily activities (insecure) to your manager (trusted). 

One concern you may have is that writing insecure information to a secure place could lead to problems. These problems would be related to integrity. An integrity violation occurs when bad data from an untrusted source is written into a secure variable. If the data isn't checked for validity, it could mess up programs running securely.