In plain English: Options are basically a contract, with a time limit, that states the holder can buy a certain amount of stock at a certain price. "Options dealers" are the people who wrote the contract and sold it to another party. They are on the "hook" for fulfilling the terms, if the buying party wishes to "exercise" an option and buy their promised stock at the promised price.
Options dealers are automatically "short" all of the contracts they sell, because that's literally the definition of "shorting" -- selling something you don't own. Options dealers technically do not own the stock they're promising to sell to the buyer, but will have to once the buyer "exercises" the options contract.
Delta is basically the difference in velocity of the price of the options contract vs. the price of the stock it's representing. So, if the option is selling for $10, and has a delta of 1 (100%), then a $5 increase in the stock price will increase the option contracts price by $5 to $15. If the delta is 0 (0%), the price of the contract will not change.
Actually, I was wrong. The GP was correct to use the vocabulary he did -- because what I wrote isn't even the full explanation I was planning. However, three paragraphs in, I realized it would take much more to completely explain it.
Basically, options dealers hedge by buying the stock they issue options contracts for, and this can cause the price to move up.