What are LDUs and how do they relate to LEGO bricks? What are LDUs? I see technical people talking about plans and designs in terms of LDUs. I understand it's a measurement unit.

What does it mean and how do LEGO bricks relate to them? Why are they needed?
LDU stands for LDraw Unit - the basic unit of measurement in LDraw, the open standard for LEGO CAD programs, and map to the "Fine" grid setting in applications such as MLCad.

Common measurements include:

1 brick width/depth = 20 LDU
1 brick height      = 24 LDU
1 plate height      =  8 LDU
1 stud diameter     = 12 LDU
1 stud height       =  4 LDU    



A 1x1 Brick as 3 Plates in LDUs (via LDraw)

The typical LU (LEGO Unit) measurements are coarser at:

Brick height = 6
Plate height = 2
Stud pitch   = 5


Based on the physical dimensions of a LEGO brick, this means that 1LDU == 0.4mm, based on a stud height (1LU) of 1.6mm.