This is not what you think. For people who played the first Monster Hunter game, there will be elements that is part of the norm. Well, even though your hunting monsters, you'll actually hunt for creatures, whether it's dinosaurs or animals fictionalized for this purpose.
For new players, you should obviously create your own person that you would like to take on the open-ended quest, both offline and online. Ideally, to get the hang of the game, after you create your person, you can by and sell weapons and most importantly, by armor because the creatures in the game can kill you forcing you to start over from the save point.
Your not just fighting creatures, you may have to capture creatures as well, depending on the requirements on your mission. Also, certain missions wants you to gather resources for a certain purpose. When you're not in action, you can eat food to enhance endurance, stamina and perhaps upgrade your health as well. From time to time, you'll also need to sharpen your weapons or else it won't impact the creature your fighting against.
Most importantly, you can take your person online for a co-op adventure. But if you're playing the Wii version, you have a limited time until April 30th 2013, forcing you to stick to offline play. To continue your online experience, only the Wii U version allows you to continue your online adventure at this point.
Perhaps to end the confusion, even though it is a role playing game, the only element not part of it is gaining experience. You instead need to get better weapons and armor as you tackle tougher challenges as you progress, and also time your attacks as the weapon of choice has its own sense of rhythm. Practice makes perfect.