The Kalm traveller can be found in the rightmost building in Kalm on the top floor. If you see him after Meteor is summoned, he mentions three items that he would like to find. The Guidebook, the Desert Rose, and the Earth Harp.

It's important to see this guy if you want to defeat the Emerald Weapon. If you bring him the Guidebook, he'll give you the Underwater Materia needed in order to eliminate the 20 minute timer during your deep-sea battle with the Emerald Weapon. How do I get the Guidebook, you ask? Well that's simple. Sort of...  You'll need to morph a Ghost Ship, the big ugly skeletal pirate ship you find in the tunnel to the underwater reactor. This guy's a pain in the a** because he uses his Goannai attack to knock your party members out of the battle. If he throws out the one who has Morph equipped, you'll have to defeat him (or run) and wander around the tunnel until you find another one. If you're not sure how Morph works, it's fairly simple, just a little tricky. You have to hit the monster with Morph when his HP is low enough that the hit will finish him off. Instead of just fading away, an item will appear instead.

If you defeat the Emerald Weapon, you'll receive the Earth Harp. You can get the Master Summon, Master Magic, and Master Command from the Kalm Traveller.

For defeating the Ruby Weapon, you'll receive the Desert Rose. This can be traded for a Gold Chocobo, which will enable you to reach the Knights of the Round Materia on the Northeast Island. This Gold Chocobo, however, in a word, SUCKS for racing so if you want cool chocobo racing prizes you'll still have to breed your own.

More info on how to beat the weapons.