What are Qubits?

Quantum Definitions: Quantum 101

Quantum bits (qubits) are a fundamental units or building blocks upon which quantum computers are based.  
Qubits can exist in both states 0 and 1 simultaneously.  Qubits exist in a probability, or superposition, of both zero and one until you measure or observe it. 
Qubits are complex, two-dimensional vectors.  Hence, the state of a qubit is a continuum of two-dimensional complex vectors as compared to a bit which has two finite states of 0 and 1.  
 Qubits
 
The state of a single qubit can be represented in complete generality by:
where