PURPLE was the designation the Americans gave to the Japanese Type B cipher machine, and by extension to the traffic the Type B generated. This was used for diplomatic traffic. The US Army team responsible for dealing with PURPLE traffic was called Purple Section.
MAGIC was the designation for the decoded PURPLE traffic, in the same way that ULTRA was decoded Enigma traffic.
JN25 was the US Navy designation for the Japanese Navy's General Operational Code, which naturally enough was the code used to transmit Yamamoto's itinery (although it was later retransmitted in the Japanese Army air-ground code, a code so simple that experienced US cryptographers could sight-read it).
More detail than one could reasonably need can be found in The Emperor's Codes (Michael Smith, Bantam, 2000).
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This page updated Mon, September 04, 2006, around about 24:00 ish (BST).