A quantum state is the mathematical object that fully describes a quantum system, such as a qubit or a collection of qubits. It encodes the probabilities for every outcome that could result from measuring the system. Unlike a classical state, which has definite values, a quantum state can hold many possibilities at once through superposition, and can link systems together through entanglement.
When a measurement is made, the quantum state “collapses” into one of the possible outcomes, chosen according to the probabilities the state encodes. Before measurement the qubit can occupy a superposition of its basis states; the act of measuring forces a single definite result.
For a single qubit, the quantum state can be pictured as a point on the Bloch sphere. Preserving a well-defined quantum state long enough to compute with it is the central engineering challenge of quantum computing, since unwanted interaction with the environment degrades the state through decoherence.