'The character's will or faith can sustain him where his flesh fails. He ignores the effects of injury, Fatigue, and Stunning during combat. This talent does not prevent the Damage, but allows the character to temporarily ignore its effects for the duration of the combat. Death still effects him normally.' -Deathwatch, pg. 116

Am I to understand that this ability renders the Space Marine immune to the effects of all critical damage during combat other than death? And if so, how does this work after the combat is over? Obviously an arm that suffers a critical explosion effect doesn't suddenly explode after combat is over.

Much like stimulant effects, this talent allows a player to ignore what could be called status effects from critical damage. It does not, as the description states, prevent the actual damage.

A character with this talent would ignore effects like: Fatigue, loss of actions, and/or unconciousness.

What the talent does not ignore includes: Actual damage (a character taking 5 crit damage is still at 5 crit damage), limb loss (your limb is gone when you take the damage, if a test is required to avoid dying immediately it is postponed until the end of combat though), or physical effects such as being knocked down or slipping on blood.