The discrete Fourier transform (DFT) is the traditional method employed to compute the frequency spectrum of a discrete digital signal. DFT can be seen as a series of notch filters centered around frequency bins that are uniformly distributed along the frequency axis, and of constant width.
The quality factor of a resonant filter, commonly denoted as Q, is defined as the ratio of its bandwidth relative to its center frequency. The DFT process is therefore analogous to a variable Q filter-bank: in other words, its frequency resolution is constant across the spectrum. When applied to sliding blocks, this process is called STFT, for Short-term Fourier transform.
Although convenient in terms of computation, this can be seen as less than ideal for many audio applications, for several reasons, the first and foremost being that human perception of frequency is known to be quasi-logarithmic. Logarithmic means that a two-fold increase in frequency translates to a one octave shift, a four-fold increase as a two-octave shift - and not four as this would be the case, were our perception linear in nature.
Pure Analyzer employs both standard DFT and proprietary algorithms that more closely model the human perception. In addition to greatly improving the legibility of the resulting curves, this proprietary transform has the additional benefit of reducing sensitivity to noise in the high-frequency portion of the spectrum especially, and provides more stable readouts.
You can of course switch back to standard DFT by disengaging the Pure spectrum button.