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Backtracking is used in a declarative type of programming language that will allow for more than one solution to be found, if a solution is found/not found the program will ‘backtrack’ and explore other paths/possibilities to try to find alternatives. http://www.cis.upenn.edu/~matuszek/cit594-2012/Pages/backtracking.html
Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons each partial candidate c ("backtracks") as soon as it determines that c cannot possibly be completed to a valid solution.
The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of k queens in the first k rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned.
Backtracking is an important tool for solving constraint satisfaction problems, such as crosswords, verbal arithmetic, Sudoku, and many other puzzles. It is often the most convenient (if not the most efficient) technique for parsing, for the knapsack problem and other combinatorial optimization problems. It is also the basis of the so-called logic programming languages such as Icon, Planner and Prolog.
Backtracking, if you're interested in studying further, is a hot topic. Check out the following:
Backtracking: Wikipedia link
Top 20 Backtracking Algorithm Interview Questions