The Hadamard gate is a fundamental quantum gate used in quantum computing. It transforms a qubit's state by creating a superposition, allowing it to represent both 0 and 1 simultaneously. When applied to a qubit in the state |0⟩, it changes the state to (|0⟩ + |1⟩)/√2, and when applied to |1⟩, it results in (|0⟩ - |1⟩)/√2. This gate is crucial for quantum algorithms, as it enables the exploration of multiple possibilities at once. The Hadamard gate is represented by a specific matrix, and its operation is reversible, making it an essential component in quantum circuits and computations.