What do the backpackers take in their backpacks? Where do they sleep and what do they eat?
"Backpacker" is really just a (somewhat dated and slightly pejorative) term for "cost-conscious traveler," one which derives from their usual choice of luggage.
The logic is simple: as a savvy but less-than-rich wayfarer, you'll have to carry everything with you all the time, so pack light! Also, you'll need your hands free for other tasks.
"Why Buy A Backpack?"
Finally, the idea is that you hope to be able to cram the thing into an overhead compartment on an airplane (harder and harder these days, but that's the idea).
As well as on trains, buses -- in short, it never leaves your sight until you lock it up in your next room, perhaps in a locker if it's a dormitory style arrangement (such as in a "youth hostel," another out-dated term.
They're now generally just called "hostels," without the "youth" modifier appended, except in a few places, like Bavaria in Germany, which might still actually turn away anyone over their mid-twenties.
Of course the only real valuables you should have with you include money, bank cards, plane tickets and other essential documents, which stay in a money belt around your waist at all times, except in the shower.
When they might very well still be on some kind of hook (maybe even the shower-head itself) within easy sight distance, and away from pawing hands other than your own.
So you see that backpacks are full of clothes, perhaps also a travel guide or two, a first-aid kit and other such replaceable things
Possibly including electronic devices bought locally for use only while you're there (don't bring your expensive iPad with you to the Third World!).
As for where backpackers go, the short answer is: they go anywhere other travelers go. There is no good reason not to go anywhere you would go if you had more money; you just need to plan to spend less time in places which are more expensive.
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May I recommend a book at this point, "The Practical Nomad: How to Travel Around the World," by Ed Haschbrouck. Rick Steves' stuff is also quite good, but he's definitely "Euro-centered," so you'll need to look beyond him if you're headed farther afield.