The higher the curve the more sensitive the film reacts to the corresponding wavelength. If you take FP4+ for example, this film is less sensitive to the blue part of the spectrum (400-500nm) than it is to the red part (600-650nm). The light of the wavelength the film is more sensitive to appears brighter in the final print. Older films from the pioneer era of photography were very sensitive to blue light, thus blue things became disproportionately bright in the print. The sky, for example, often became just a bright and uniform area. A dark-yellow filter was needed during exposure to separate it from the clouds. With FP4+, such a filter is not really necessary and if it is used, the effect will be more dramatic. On the other hand, the spectral sensitivity of FP4+ ends abruptly around 650nm, meaning this film is not sensitive to infrared light. If you look at the charts of infrared film, you will see that their graphs go far beyond 650nm.
To sum it up, these charts are pretty useful to judge how a film will convert real colours into different shades of grey and how it will respond to colour filtration.
Edit: This only refers to the Spectral Sensitivity. For the Characteristic Curve, see the posts below.