Although the network problems over Christmas were caused by a hacker group, Sony has still responded with their apologies, and they are working to set up counter measures that will stop this sort of attack happening again in the near future.
To top it off, the FBI have confirmed that they are actively searching for the origins of the Lizard Squad hackers, so hopefully they will get what's coming to them.
As for the compensation, firstly all PS Plus members will receive a free five day extension to their current membership - this may not sound like a big deal as it's likely most players have already got their membership set up to recur each month. It is however a nice gesture from Sony, and the second part of the apology package will probably be a lot more appreciated.
For the entirety of January, all PSN users, including those without a PS Plus subscription, will be given a one time discount code for any digital item within the PS Plus store. The discount code will offer 10% off, and it can be applied to your shopping cart, allowing you to potentially save 10% on more than one item by purchasing several games in one order.
So far Sony have not revealed when the discount code will be available, but it should be fairly shortly.