The floor press targets the shoulders and triceps in the specific way they will be used in the benchpress.
The specific part of the strength curve the floor press works depends on your body mechanics. For some the weight is only slightly above the chest in the bottom position. For others it is 3 or 4 inches up. You will need to experiement with this lift to decide whether or not it is for you.

A palms facing grip is
used to bring the triceps and shoulders more into
play. Dumbells are lowered until the upper arm rests
on the floor
 
 

The chest is then relaxed to remove the
existing muscle tension, dumbells are then pressed up
to lockout.  If one wanted to increase the range of
motion, these can also be done while lying on a raised
pad

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Many thanks to Donna Slaga for providing the photos and description