The Kahneman-Tversky value function is a crucial element of Prospect Theory that describes how people perceive gains and losses, emphasizing that losses typically have a greater emotional impact than equivalent gains. This function is concave for gains and convex for losses, illustrating that individuals are risk-averse when it comes to gains but risk-seeking when facing losses. The shape of this function highlights the concept of loss aversion, where the pain of losing is psychologically more powerful than the pleasure of gaining the same amount.