Superposition

A superposition is a linear combination of basis states. For a single qubit, that is a combination of the two levels, with complex amplitudes whose squared magnitudes are probabilities when the qubit is measured. For several qubits the same idea applies to the full computational basis.

The phrase "tries every input at once" is the version to retire. A superposition gives a quantum algorithm amplitudes it can interfere. It does not yield every answer as a classical list. Grover's algorithm starts from the uniform superposition so that a later reflection can increase the amplitude of marked items. The speedup is in the number of oracle queries, not in a simultaneous readout of every database entry. Nielsen and Chuang develop the linear algebra; the algorithm page is where the interference is put to work.