Delta (Δ) is a risk metric that estimates the change in price of a derivative, such as an options contract, given a $1 change in its underline asset.
Delta neutral is a portfolio strategy utilizing multiple positions with balancing positive and negative deltas so that the overall delta of the assets in question totals zero. A delta-neutral portfolio evens out the response to market movements for a certain range to bring the net change of the position to zero.
Beta weighted Delta is a means for investors to put all of their positions into one standard unit. It is a way to look at an entire portfolio and understand how it will change with a move in the market. It tells us about the size, diversity and general volatility of our positions.