The template
Choose → explore → un-choose. At each step you make a choice, recurse, then undo the choice before trying the next. A 'prune' check skips branches that already violate constraints, which is what makes backtracking tractable despite exploring a combinatorial space.
Recognising it
Backtracking fits 'generate all/return any valid configuration' problems: subsets, permutations, partitions, placing queens, filling a grid. Complexity is usually exponential in the worst case, so pruning early and ordering choices well matter.