When entering into a short or leveraged position on dYdX, one of the things happening behind the scenes is a buy or sell of the underlying asset (e.g. if shorting ETH, ETH will be borrowed and sold for DAI).
Spread: The difference in price between the highest bid (the price a buyer is willing to buy for) and lowest ask (the price a seller is willing to sell for) an asset.
Price Impact: The extent to which the price moves given the size of your order. For example, a larger order will cause the price to slip more.
Max Slippage: The maximum amount of additional slippage beyond the expected price impact that will be allowed on the product. If the slippage exceeds this amount, the order will fail in order to protect the trader from a bad price.
The reason that the price can slip beyond the expected price impact is if the market moves during the time it takes the user to place the order and for the transaction to mine.