The fat lighter replaces typical kindling. For starting a fire in the fireplace I'd put a sliver or two of fat lighter in, then a couple of dry split oak, then put a couple of wads of newspaper under that. The big difference is that you need less fat lighter than kindling and the fat lighter is much less fussy than kindling.
For an outdoor fire, I start with a chunk of fat lighter, pile whatever you have on top of that green, cured, wet, or whatever, give it a splash of diesel, instant bonfire.
A fat lighter knot will also make a decent torch in a pinch. BTDT.