garage threshold concrete
That gap is to relieve stresses due to expansion/contraction caused by temperature changes.  It's not a thermal break.  You need some kind of flexible filler to keep water from getting into the gap, freezing, and cracking the concrete.
There are numerous materials than can be used to fill in the gap, so it's hard to say what may have been used in your case.  Looks like it may some sort of tar/oil impregnated material.  It's usually the depth of the concrete pour, probably 4&quot;-6&quot;.