Why did the rifle have two triggers?

I'm not a gun expert, but I think that the first trigger is a type of safety mechanism. At long range, just a tiny error by the shooter can result in the bullet going well off-mark. The trigger that actually fires the rifle won't work until the first trigger has been set, lowering the chances of accidentally firing the rifle before one intends to. Mounting the safety just ahead of the trigger makes the process of moving from one to the other smoother than it would be if the shooter had to move his hand to unlock a safety mounted on the said of the rifle.

- You may have come on no bicycle, but that does not say that you know everything.

A double set trigger allows the shooter to pull the trigger in the forward position first which results in the rear trigger now being very light and easy to pull. http://www.hallowellco.com/double_set_triggers.htm

This is essential for accuracy. Modern triggers are made better so they don't need this feature.

Ranb

The rear trigger cocks the hammer. It does it smoother than cocking the hammer with your thumb.

ranB40 above is correct.

Look at this way: it's kind of like rolling a heavy bolder to the edge of a cliff. Once you get it to where it's just barely balancing on the edge, a much smaller effort is required to get the bolder to fall.

So if it had only one trigger, a much stronger finger pull would be required to get the hammer to the precipice of firing. With a two trigger setup, you pull the first trigger without worrying about throwing your aim off. Once you aim, the tiny bit of finger effort will release the hammer and won't throw off the aim.

Best way to describe it is how it actually works. The sear is the part that keeps the hammer from falling. For safety, the sear sits high and protects the gun from firing if dropped or otherwise abused.
When you pull the set trigger, it effectively half drops the sear making it much more unsafe. Now, the forward trigger will break like glass with no creep. You can pull the trigger with strand of hair now.
If you use an old rifle with a 2 stage trigger, you can see what it's doing. Like an M95 Steyr-Mannlicher or a K38 Swiss. The first pull takes up the slack on the sear. Once you feel the second stage, it breaks very clean and light. Just not as light as a double set trigger.

It's so that you can safely have a "hair trigger", i.e., a very light, zero-creep, breaks-like-a-glass-rod trigger. With double-set triggers, the trigger that fires won't do anything unless the other trigger is pulled first, which adds a considerable margin of safety.