I understand that the yeast activates, but why does this happen? Is the water simply absorbed into the yeast?
I presume you're talking about active dried yeast. In that case, the granules of packaged yeast have some nutritive content to them, so what you observe when you add warm water is a weak form of priming. Priming is the addition of both warm water and a food source, typically sugar or flour, to dried yeast with the goal of 'waking-up' the yeast from their dormant, packaged state. The warm water dissolves some of the food in the granules and warms the yeast up to a temperature which is favourable to fermentation.