How to interpret these filter coefficients?
Sorry, but that does not make any sense


A 3rd order BW lowpass can be described most simply with a single number: the cutoff off frequency
It's the not numerator a denominator since this would have 4 numbers and the numerator would have the shape of x*[1 3 3 1] and the denominator should start with 4.
It's not the poles and zeros since all the zeros are at -1 and one pole is conjugate complex 
It sure as heck isn't state space either
The transfer function is a boiler plate text book copy and also mostly wrong for a third order BW (which has one biqaud and one single real pole section).


You are not missing anything obvious and having you guessing blindly doesn't serve any useful purpose. You have to get back to the client and tell them that you need proper specification or you can't get the work done.