The reason for this lies within the tonic water. Tonic water will fluoresce under ultraviolet light (UV light) because of the presence of quinine. The sensitivity of quinine to UV light is such that it can appear visibly fluorescent in direct sunlight. Some say that the reason we find things that glow under UV light fascinating is because we cannot see the UV light they absorb but can see the visible light they emit.
So, why does quinine absorb UV light (the invisible component of sunlight that produces sun tans and sunburns!)? It is due to the structure of the quinine molecule, which enables it to take in energy in the form of invisible UV light and immediately radiate some of that same energy in the form of visible blue light.
If you want to get a bit more scientific about it.... quinine contains rare earth compounds called phosphors. These are the substances which glow when they are hit with particular wavelengths of the EM spectrum, including UV light. Phosphors absorb UV light and then emit it in their own colour, in this case glowing blue light.