SerialX, your shares should trade on the asx. I'm assuming you have the offer because you already hold some of those shares. The non-renounceable part refers to the actual entitlement. For example, you will notice that some stocks have rights issues and the rights are traded for a period of time (with the company code and an "R" at the end) whereas others don't allow the rights to trade. The ones that don't trade are non-renounceable. So you have 2 options - either let them lapse or take them up. Whereas IF you had a renounceable issue, you would have the 3rd option of selling your entitlement onmarket. Hope that makes sense.
The other scenario, if you don't already hold the shares, is that one of your companies is doing a spinoff.
Given it's an asset you already own, you should have some idea of whether you want to invest more in it or not. For more specific comments, it's probably best to go to the stock threads.
