It's hard to answer your question without giving a course in QM, but this is a good place to share a pet peeve about this. For some deeply unfortunate reason, "amplitude" can refer to:
(1) The (complex) coefficient of a component of a state vector.
(2) If we treat that number c as re^(iθ), then r is sometimes called c's "amplitude" (though it's more often called the "norm" or the "modulus").
(3) Some authors even use it to refer to θ ("The argument is sometimes also known as the phase or, more rarely and more confusingly, the amplitude" [1])
Luckily, in quantum mechanics, they almost always mean (1). That's the usage here.
(1) The (complex) coefficient of a component of a state vector.
(2) If we treat that number c as re^(iθ), then r is sometimes called c's "amplitude" (though it's more often called the "norm" or the "modulus").
(3) Some authors even use it to refer to θ ("The argument is sometimes also known as the phase or, more rarely and more confusingly, the amplitude" [1])
Luckily, in quantum mechanics, they almost always mean (1). That's the usage here.
[1] http://mathworld.wolfram.com/ComplexArgument.html