A delta of 2 means that in the current state, a $1 price rise in AAPL results in a $2 profit in the position. To remove this imbalance, you need to couple the current position with yet another position inversely correlated, the "hedge."

You need a position that will have the exact opposite directional effect as the current position (the new position must lose $2 for every $1 price rise in AAPL). The simpliest way to acquire such a position is shorting 2 shares.

One share of stock will rise in value by $1 for every $1 rise in the underlying price. If you short one share, your position will fall by $1 for every $1 price rise in the underlying. By shorting two shares, you've created a position that falls $2 for every $1 price rise in the underlying.

This is why he's shorting two shares to counteract a +2 positional delta.

(Note that delta is a point-in-time value. It's not a constant. Gamma will tell you the slope of delta against underlying price change, which itself is a slope. By watching your positional gamma, you can ready yourself for further delta hedging as a result of positional changes.)