For example, my Sharp NT175-U1 moncrystalline panels have an individual cell efficiency of only 16.2%. (overall panel efficiency is only 13.5%) The rest is converted to infrared and is either reflected or passed through the panel. But really, I find it silly that it even matters when your energy source is unlimited. What does it matter if a panel passes on a significant amount of available energy, as long as you get the watts you're trying to extract. I saw one online seller pushing (more expensive) panels with slightly higher efficiency ratings, of similar wattage output. To the consumer, panel efficiency really means nothing as long as you're getting the advertised watts.

Now, one reason higher efficiency helps is watts per square foot. If you can get more watts out an array on a limited amount of roof space, this is a good thing, but closely note the article says "concentrated sunlight." That means they are directing an area of sunlight larger than the array itself. (probably with mirrors) I could do the same and boost my performance, but at the cost of additional heat risking damaging the panels and no doubt, shortening their lifespan.

Help me understand the significance? What is the efficiency of the "normal" cells we can buy?

The mars rovers that lasted years longer than expected had solar panels with 27.5% effeciency at beginning of life.