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From the Wikipedia article for the movie, Memento:
The purpose of the fragmented reverse sequencing is to force the audience into a sympathetic experience of Leonard's defective short-term memory, where prior events are not recalled, since the audience has yet to see them.
What about Irréversible's reverse chronology?
As the name suggests actions you make in life are irreversible, one action leads to another and you can't go back to change them.
This film analyzes what actions lead to the brutal actions of Marcus (Vincent Cassel).
Doing this in reverse order forces the viewer to reevaluate his view of Marcus, because in retrospect his actions can be justified by the unfortunate events that happened to him.
Shown in chronological order this film would be a "normal" revenge thriller but the reverse chronological order gives this film a special psychological aspect.
