There are a variety of types of backpacking trips that all require different gear, but in general you are going to want a set of basic things:
You will of course want a backpacking backpack. It is important when buying a pack to know how much stuff you plan to bring with you regularly, so you can adjust for size. You will also want to get straps around the hips (a normal backpack will not do). The most important thing about buying a backpack is comfort, so make sure you like the way it feels.
A sleeping bag is very important for backpacking. It depends on where you will be trekking, but you will want to make sure that your bag is good for the temperature you will be staying in. If most of your hikes are in the summer and it stays warm at night, a 40 degree bag may be all you need. If you plan to do some winter backpacking, you might need something as warm as -15 degrees. There are synthetic bags and down bags, both have pros and cons and are to your preference.
A sleeping pad is one of the most important pieces of gear to take with you when backpacking. It may seem like a luxury and is strictly for comfort from the hard ground. It does provide softness, but the main thing it provides is warmth. A sleeping pad insulates you from the cold ground and is equally as effective at keeping you warm as a sleeping bag is.
A tent isn’t always necessary. In warm climates and during dry months many people choose to sleep under the stars. However, a tent can provide great shelter and warmth during storms involve wind, rain, or snow. Having a tent could be the difference between life and death in some extreme situations.
Having good boots is a basic necessity for backpacking. A good pair of boots will give you some many advantages. Most backpacking boots are lightweight and durable. They have good traction and are super comfortable. They provide you with great ankle support that is necessary for when you are carrying your pack, and many boots are waterproof, keeping your feet warm and dry for your entire adventure.
There is clearly more to backpacking than just these few items, but with the things discussed above you would be very well off in the wilderness. I will post another article that breaks down other things that are needed when going on a backpacking trip.