This demo:
1. Performs a Fourier transform on some image pixels, taking the pixel data from the "time" domain into the frequency domain. (Think of time as "how far through the image we are", and the pixel's intensity as the signal's magnitude; frequency in this case becomes a slightly abstract concept.)
2. Visualises that frequency domain in various ways - by default you're seeing the magnitude of the transformed signal
3. applies a band-pass filter to that frequency domain - i.e. only allowing signals above a certain frequency (low-cut) and below another certain frequency (high-cut), and removing the rest. Playing with this might give you an intuitive notion of what "frequency" means here.
4. applies the inverse transform, giving you a signal back in the time domain (i.e. a normally viewable image).
You can see what the effect of bandpassing the frequency-domain signal is on the end result. Thinking about it in terms of Information, if we band-pass half of the given frequency spectrum out, we're essentially throwing away half of the Information... but yet the image is still useful to a human (this is the principle of how lossy compression algorithms work, as others have noted).
[0] In the case of a "perfect" transform, in reality most algorithms are lossy