Can anyone explain what the first half of this sentence means?
The NYSE has guys (mostly guys) who stand around on the floor and act as market makers for various stocks. They call 'em specialist. They stand around and run the auctions for shares, match up bids and so on. Basically, they make sure that if you want to sell a stock, there is somebody buying, and vice-versa. This is their business, and they can't just throw up their hands and wander away, ruining the market in some given stock.
The high-frequency traders provide a similar function in electronic exchanges. However, they all threw up their hands and walked away, exacerbating an already bad situation as the liquidity left the market.