FFT of square wave - what does output represent?
Simply put, a square wave can be decomposed into a weighted summation of series of sine waves, which is exactly what the Fourier transform does. Here are two animations that describe the synthesis of a square wave by accumulating sine waves.


The amplitude of FFT results are the weights of each sine waves. As seen in Fig.1, the first order harmonic has the largest weights, that's why the first bin has the highest amplitude, and the following bins have decreasing amplitudes.
An ideal square wave with an amplitude of 1 can be represented as Fourier expansion:
$$
x(t) = \mathrm{sgn}(\sin\omega t) = \frac{4}{\pi} \Big( \sin\omega t + \frac{1}{3} \sin 3\omega t + \frac{1}{5} \sin 5\omega t + \ldots \Big)
$$
The above equation shows that the ideal square wave contains only components of odd harmonics and their amplitudes are decreasing. However, in real world square waves contain all integer harmonics.
Bin 0 represents DC (direct current, i.e., 0 Hz). Since your square wave has a zero mean, the DC components is zero as well. Try to add a constant value to the original square wave, then take FFT and see what happens.