Ever since I was little, I’ve associated colors with objects; a vibrant, brilliant red for apples, a mellow yellow for bananas, and a deep purple for my favorite eggplant dish at home. To many, color conveys more information than just a specific wavelength of light; it is deeply linked to the emotion and senses. In some ways, color adds dimensionality to understanding. However, sometimes the way we sense color can get mixed up with the other senses.
Synesthesia is a neurological condition that mixes sensory stimuli together. Formally described as a perceptual phenomenon in which stimulation of one sensory pathway leads to involuntary stimulation of another sensory pathway, synesthesia is a poorly understood process that has caught my attention in a field focused almost exclusively on problems of the brain. An outlier to these pathological conditions, synesthesia stands out as a fringe trait in biology with no apparent benefit that has persisted through the ages.
While the idea of synesthesia is simple, an unintuitive aspect of synesthesia is that it is incredibly consistent. For example, in grapheme-color synesthesia, the most common form of synesthesia where words and numbers stimulate visual pathways for color, the letter A might always appear red to the synesthete. If you went on to test the synesthete at intervals in the future, the letter A would consistently register red. To me, this consistency feels almost algorithmic, its simplicity understated as a lucid example of neural network interference. Although many brain studies try to boil neural networks down into simple circuitry (like what @gillichu is trying to do!), many get lost in the detail, a natural result of working in complex systems. In this case, I would be interested in seeing synesthesia as a model for examining basic neural network construction.
Moreover, another overlooked characteristic aspect of synesthesia is that it is generally automatic. This aspect is tested via a modified Stroop test. 
For individuals without synesthesia, describing the color of words that have no relation to color is usually quite simple. For example, the word hollow colored orange would be simple to describe as orange. However, if you had grapheme-color synesthesia that already painted words distinctive colors, you could possibly find that words like hollow colored differently would make you pause. Using this test, researchers have evaluated the time taken to conclude the color of the word as a proxy for the difficulty of the task and determined that synesthete lack control over their almost preternatural ability.
In terms of development, synesthesia is thought to develop during childhood as children begin thinking abstractly.  Abstraction, or thinking of the world conceptually, is a process that generally develops in childhood and adolescence, when semantic networks in the brain begin to edit themselves. This hypothesis, the semantic vacuum hypothesis, possibly explains the predominance of grapheme-color synesthesia. As a child, one of the first abstract concepts that we grapple with are numbers and letters. I remember struggling with the concept of negative numbers when my mom introduced them to me, not able to picture values on the other side of the number line and ended up repeatedly adding their positive counterparts together. For synesthetes, this process of building abstract concepts also comes with the side effect of synesthesia. For this reason, synesthesia has been strikingly important in helping scientists understand how we perceive the world and conceptualize it. 
Finally, I’m really excited to learn more about synesthesia. Color plays such an integral role in processing information and is a really cool stimulus to study. Stay posted to learn more about seeing sounds and creating color!