Let's understand this principle with a simple example.
When designing an application, you need to have the user enter a login name and password. The function that performs the work of getting and checking the password is called, let's say, mygetpass(). It's invoked by the mylogin() function: mylogin() → mygetpass().
Now, the protocol to be followed is this: if the user gets the password wrong three times in a row, the program should not allow access (and should log the case). Fine, but where do we check this?
The Unix philosophy: do not implement the logic, if the password is specified wrongly three times, abort in the mygetpass() function. Instead, just have mygetpass() return a Boolean (true when the password is right, false when the password is wrong), and have the mylogin() calling function implement whatever logic is required.