A 50/50 stock-bond portfolio is not 50/50 in risk terms — stocks contribute roughly 90% of total volatility. Risk parity inverts this: weight positions by their contribution to portfolio variance, not by their dollar allocation.
For a retail investor, a usable approximation is to size positions inversely to their volatility. A US equity sleeve at 15% vol and an emerging markets sleeve at 22% vol should not be sized equally — the EM sleeve should be roughly 70% of the US sleeve in dollars to contribute the same risk.