Fourier Spectra : Significance of the Negative Amplitude
Note that in general the Fourier transform of a function is a complex-valued function, so in general it is not only positive or negative.

Roughly speaking, the magnitude of the Fourier transform says something about the presence of certain frequencies components in a signal, regardless of the phase (or sign, in the real-valued case). The phase determines the temporal alignment of the different frequency components. So a real-valued negative value of the Fourier transform just implies a 180 degrees phase shift of the respective components.