Up till now we've mostly talked about using a tripod in terms of getting slower shutter speeds to help you blur things. This photo certainly uses that technique - if you have a look at the small waterfall there you can see that it's been blurred by a slow shutter speed.
But the main reason for using a tripod in this situation is to increase the depth-of-field - what is in focus from foreground to background. To get everything in the frame in focus you have to use a small aperture - f16, f22 somewhere around there.
The problem is that when you close your aperture down so small you get a really, really slow shutter speed. And when that happens if you try to handhold your camera you're not going to have just a blurry waterfall, you're going to have a blurry everything!
Add that to the fact that when in the rainforest you want to be using a polarising filter to cut down on reflections and bring out the lush greens. Stick that filter on and you're going to lose two stops of light and get an even slower shutter speed. We could be talking up to 30 seconds or so.
So that's when the tripod comes out. Just a word about tripod technique. I see a lot of people who stick the camera on the tripod and then try and compose the picture. As a result most of their photos are taken at exactly tripod height, and usually horizontally! :) It's much better to leave the camera off the tripod and work out your composition first, and then adjust the tripod to fit where you want to be.