Can you explain what the flux of a light source is?

The word 'flux' can be used in many different contexts, but in general it refers to the amount of 'stuff' passing through a unit area of space per unit time. In the case of light sources, we can measure flux in units of joules per metre squared per second (Jm^-2s^-1). Looking at units is often a good way to work out what something means, in this case we are told that the flux is the energy passing through a one metre long square at the point of measurement every second. The energy is originating from the photons emitted from the light source, hence the more photons there are passing through that metre square the bigger the flux will be. We can even change the flux to measure the number of photons passing through the square, rather than the energy, by dividing by the average photon energy. So in short the flux of a light source is simply the 'amount' of light passing through an area of space in a set amount of time. 

The flux of a star is a very important quantity in astronomy. It is related to the luminosity of a star (the total power emitted per second) via an inverse square law, hence the flux will become smaller the further you are from a star. This means if we know the luminosity of a star, or any cosmological object for that matter, and measure its flux, we can calculate the distance to the star. This is also true for light sources on the Earth, but we can normally just measure those distances with a ruler!