Delta neutral refers to a position or portfolio which has an overall delta value of zero or very close to zero. This means that the portfolio does not react to small changes in price of the underlying assets.
When a position or portfolio is delta neutral, not only does it not react to small changes in the price of the underlying asset, it is also able to profit when the underlying asset breaks out in price, no matter to upside or downside. Yes, profiting both to upside and downside.
Delta neutral is especially useful in options trading when positions are set up to take advantage of time decay. When a position is designed to profit through time decay, it needs to react as little as possible to changes in the underlying asset as possible. In order to do so, a concept known as dynamic hedging is used where the overall delta value of the position is rebalanced whenever it moves out of neutrality.
Delta neutral hedging can be attained using options, futures, stocks or any combination of them.