The Nash solution in bargaining, like negotiations about wages between a company and a union, is important in real-life situations. It was developed by John Nash in 1950 to solve bargaining problems using a rule-based method instead of looking at specific offers and counters. This solution aims to find mutually beneficial outcomes for both parties by following specific principles, narrowing down options until a fair solution is reached. The focus is on reaching agreements that benefit everyone involved without looking at it as a win-lose situation.