Thanks for your interesting question. In short a bumper absorber is
there to absorb an impact which the bumper assembly itself can't.
Here is a longer explanation...
"The bumper absorber is a Styrofoam or plastic piece which is usually
placed between the bumper cover and reinforcement to help absorb
impact. As mentioned above, the bumper cover goes around and covers
the front end while this reinforcement is a metal or aluminum bar
which is mounted on the car frame. Sometimes, impact during collisions
is so strong that the bumper alone cannot take this. That is why this
bumper absorber, as the name implies, helps absorb some of this impact
to better protect the front end of your vehicle. By absorbing the said
impact, less damage can be done to the vehicle, and so the car owner
will not have to spend so much on replacement parts such as the
headlight and grille"
So yes, it would appear that this is the white styrofoam that you see
through the crack in your bumper. If you need anything cleared up,
please request a clarification and I will be happy to help.