I am not sure that I would recommend sending an inexperienced skier off into even "side-country" without some avy skills and the proper gear....see the posts about "Lost for 10 days...fought off wolves...one dead". That may have been a side-country trip gone bad.
Here is a basic primer on AT and telemark...
Both telemark and AT gear allow a skier to climb uphill with their skis on. To do this, both AT skiers and telemark skiers use skins, which allow forward movement but retard backwards movement of the skis on snow. If you are familiar with fishscale XC skis, the principle is the same, but skins are far more effective. Climbing with skis and skins allows a backcountry skier to cover significant distances in deep snow, where bootpacking is not practical. Even snowboarders can get into backcountry using a split-board, a snowboard that is cut lengthwise down the middle and used like skis for uphill travel, and then clamped back together for downhill travel. For all of these modes, the key is being able to lift your heel when climbing.
Telemark boots and bindings accomplish this by letting the boot bend at the forefoot so you can lift your heels. AT bindings do this by hinging at the toe, and releasing the heel piece from the ski. Some telemark bindings can also hinge at the toe, providing even more range of motion during the climb. The difference between the two is that telemark skiers leave the heel free during their descent, while AT skiers clamp their heel down to descend.
You may see telemark skiers at a resort, too, riding lifts and otherwise doing the same things as regular skiers. The difference is one of technique, although with modern plastic telemark boots and beefy bindings, many tele skiers can and will do regular alpine turns if they feel like it. I telemark, and switch back and forth between telemark turns and "regular" alpine turns as my mood and the terrain dictate. Most telemark bindings are not designed to release, although there are a handful of releaseable models.
There may also be skiers using AT equipment in-bounds. Unless you look closely at their bindings, however, you may not notice them.
Another gear difference is with the boots. Regular ski boots are not designed to walk in. They have slippery soles to enhance proper release and no ankle flex. Telemark boots and AT boots typically have vibram soles so they can be used to scramble over rocks and other mountain terrain. Telemark boots have a bellows at the forefoot so they can bend, and some have a "walk" mode, which releases the connection between the ankle cuff and the lower boot. Most AT boots also have a walk mode, too.
As others have suggested, both AT and tele gear are tools for accessing the backcountry. However, to be safe, you need other tools, probe, shovel, beacon, emergency survival gear, and perhaps an avalung, which is a device which can extend survival time for a buried victim who is not already dead from trauma.
If you are interested in backcountry skiing, and unfamiliar with any of this, the best thing is to hire a guide service to give you a managed taste of what it is like. At Alta there is a group which takes you out of bounds from the top of the lifts, where it is possible to bootpack up a relatively short distance and get to interesting terrain. Other western resports may have similar services available.
If you have the cash, cat-skiing or helicopter skiing also provide excellent ways to get a taste of the backcounrty.
good luck and be safe....
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GAWD that was funny! 
