Backpacking is all about getting away from it all and back to basics. It’s simply you, your gear, your friends and the trail.
The type of trail you backpack on will determine the type of equipment you will bring but the gist of it is that you strap a 50-100 liter sized backpack over your shoulders and you bring enough stuff to survive in the wilderness for an extended period of time. Things like clothes, a sleeping bag, a tent, some food and first aid supplies.
From a time perspective, the minimum is about 2-3 days but it can go up to much more than that as some people do it for weeks and months. Why do people backpack? Everyone has a different reason – mine is to reconnect with nature, exercise and have a chance to see natural phenomenons. Seeing Western Brook Pond, coming over the lip of Quilotoa crater, the view from atop Mt. Marcy or crossing the Logan Creek Suspension bridge is something that cannot be properly conveyed through pictures or video but the feeling you get is unlike anything else and for me and it is why I backpack.
A quick online search will get you to a site (like this one) where you can learn the ins and outs of backpacking if you want to try your first trek. I suggest that you perhaps try a 2 night trip at a nearby provincial/state park trail and go with someone who has done it before and please oh please, do not make the mistakes I did on my first real backpacking trip.