Beginner question: Let's say I make two flat panels. They are the same size, roughly as big as a regular computer monitor.

As a raw core, it certainly isnt the lightest in kg/m3  Some aluminium honeycombs with a large cell size are far lighter.

however what they probably meant is its the lightest core for its relative performance and that may well be accurate.

It is used a lot in the RC model aircraft scene too.  You can make some really light panels with a single layer of light woven glass either side of the core to give a nice stiff bulkhead panel or stiffening panel.

Warren Penalver
Easy Composites / Carbon Mods - Technical Support Assistant

You can see this type of material a lot on different expo's and so on. They use it for aero-projects and racecar-seats. mostly as a core-material to add some stiffness but keep te lightweight. 

My supplier has something called kevlar honeycomb, as far as I know it is made out of kevlar paper(?) pre-impregnated with phenol resin. It is realyyyy expensive 70euro exl.vat for 2mm x 2550mmx1250mm and 48kg/m^2, he claims that it is the lightest sandwich in the world. I don't have money to buy it, but when I have some $ I will make some reviev of that, this is how it looks like :