Back-to-Back is buying two tickets that meet the Saturday night stay requirement to circumvent the Saturday night stay requirement. So, you need to go ATL-CLT on Monday and return Friday for two weeks in a row. To buy a ticket (ticket A) ATL-CLT-ATL with those dates would cost say $1000 each. But instead you can buy two tickets, one leaving Monday and returning the second Friday ATL-CLT-ATL and another ticket (ticket B) CLT-ATL-CLT on Friday and going back the following Monday, and these tickets cost $250 each instead of $1,000 each. So, you'd use the first half of ticket A to go ATL-CLT, then you'd use ticket B to go CLT-ATL-CLT, then the second half of ticket A to go home the second Friday CLT-ATL. That's back-to-back ticketing.

Throwaway ticketing is similar except say you only need to be in CLT for one week, but you buy the same two ticket but instead of using all of both ticket you just "throw-away" the second half of each ticket. You still save $500, even though you're throwing away half of each ticket.

Hidden-city is say you want to go ATL-CLT but it's $500 one-way. But, you can can buy a US ticket going ATL-GSO and connecting in CLT one-way for $200. You buy the $200 ticket and just get off the plane in CLT and don't use the CLT-GSO portion.