This is quantum mechanics notation and basic principles. |x> is pronounced “ket x” (the second half of the intentionally-misspelled word braket), and refers to

This is quantum mechanics notation and basic principles. |x> is pronounced “ket x” (the second half of the intentionally-misspelled word braket), and refers to a quantum state x. The quantum states |0> and |1> refer to the classical states we’re used to. But as written in the GP comment, a general qubit state is given by a|0> + b|1>, where a and b are complex numbers. This is a “superposition”: the qubit occupies both states simultaneously and will resolve to one of them when observed/measured. For any quantum state written in this way, we know from quantum mechanics that observing the state will yield a measurement of the state |0> with probability |a|^2 (the norm of the complex number a), and will yield state |1> with probability |b|^2. The qubit measurement must yield exactly one of a or b, so the probabilities must add up to 1, hence |a|^2 + |b|^2 = 1.