According to DIN EN 10052 it is the margin distance from the carburized workpiece surface at which the carbon content reaches the specified limit, typically C = 0.35 %. Commonly, the carburization depth  is around 1 mm, with deep carburization it is up to 2 mm. The falling gradient of the C content from the margin to the core must not be too steep.

Rule of thumb: One annealing passage for 4 h at 930 °C results in a carburization depth of approx. 1 mm.

Additional references:
Carburization
Carburization agent
Case hardening
Hardness test