A delta neutral position can make money from change in implied volatility, change in underlying price, and/or time decay (if short options).
Implied volatility and time decay are self explanatory so let's look at a simple price example. You buy 500 shares of XYZ at $49.75 and ten $50 puts, each with a delta of -50 so you're delta neutral. You own a synthetic long straddle.
XYZ immediately drops to $48.75 with no change in IV. The put delta is now -590 (each put has a delta of -59). You now buy 90 shares at $48.75 to restore delta neutral.
Now, XYZ immediately recovers the $1 back to $49.75 so you sell the 90 shares, restoring delta neutral and booking a $90 gain. The more times that XYZ percolates up and down or down and up, the more opportunities that you have to do this. In order to make a profit, before expiration you must book gains faster than the rate of time decay.
Since this is a straddle, money is also made if there is some terrific or terrible news that drives share price dramatically up or down, outside and beyond the break even points (approximately share price + option position cost AND share price less option position cost).