I think that your question is really two different. although related questions.

The first is "Why, from a functional / evolutionary perspective, are the digits of the human hand (or any limb for that matter) different lengths? "

The second is "How are digits of different lengths generated during development?"

Since I am not really sure which questions matters to you more, I will answer both (sorry about that).

Why: The shape of the hand (forelimb) is determined by its functions -- what it has been selected to do, evolutionarily.

How are limbs formed? The limb begins as a limb bud that forms on the flank of the embryo.

Within the limb a number of intercellular-signaling systems interact to patterning the forming limb. This systems includes a number of secreted signaling proteins and intracellular gene regulatory proteins.

Hedgehog protein is secreted from the zone of polarizing activity (ZPA) and acts to establish the anterior-posterior axis of the limb.

It works in part by regulating bone morphogenic proteins (BMPs), which in turn regulate fibroblast growth factors (FGFs). Cells respond to this signaling molecules to differentiate in various ways.

This complex network (and it is more complex that I have noted here) is associated with the expression of various homeobox transcription factors that regulate proximal-distal patterning. It is this system that determines limb and digit length.