A prism is an object that 'refracts' light, splitting it in to its constituent wavelengths [colours], like a rainbow in the sky; they can be recombined by focussing back on to a similar prism. The different colours represent the various forms of artistic activity used to draw attention to climate change : the single unified theme represented by the white light emerging from the prism when the colours are focussed through it.

A prism changes the way things look. If you look through a prism you see rainbow fringes around every object. If sunlight shines through it, it makes lovely rainbow spots on the wall. There is an idiom "seeing the world through rose-colored glasses," which means seeing only the positive or optimistic things. Because a prism is associated with MULTIPLE colors, looking through a prism is something like "seeing the world through multicolored glasses." In this case, there are many ways you could "raise awareness of the region's plight." Of all the ways they could do it, they are going to use three: art, music, and architecture. The idiom is similar in meaning to some others: "We are going to look at this from the point of view of art, music, and architecture." "We're going to approach this from our personal angle, which means using art, music, and architecture."