Elmo wrote:

There's a wire crossing my concrete driveway in the slot which I tripped on
and kicked up and need to put back.

It just about fits in the groove, almost filling the groove. I think it's
for the low-voltage lights but I'm not sure what it's for.

What "material" would I use to "caulk" the wire back into the groove so
that it's protected from people tripping on it like I did?

There is a grey self leveling caulk available that is intended for
filling expansion joints in concrete that should work fine. You should
be able to find in in the concrete area at most any building supply
place.