In a very simple nutshell: to grow stronger.
It's the same way exercising makes you sweat, tired, and ache. If you don't exercise, you become weak, even though it may be relaxing to just sit back and watch television instead. If you were to go through army boot camp, sure, it will kick your butt and you'll be worked like crazy, but you will become strong. By resisting sin and enduring the hardships of pain and suffering, we become stronger and more capable in body, mind, and spirit. If everything was easy, we would just become complacent and would never grow or develop. We wouldn't learn anything from enduring pain and suffering, and the experiences that make us strong would be lost.
In terms of physical suffering, the whole reason why people experience pain is to discourage the activity that causes pain. If you didn't feel pain when you burned your hand on a hot stove, you could be burning away your entire hand and not even know about it until it was too late. If you get stung by a bee, that string of pain is an alert that your body was physically harmed.
Also, it does help to us appreciate the times when things are well and there is peace. When you overcome a sickness, heal from an injury, recoup after emotional distress, and recover from disaster, you become stronger and the next time it happens, you're even more prepared to deal with it.
