Stock options give employees the option to buy stock at a predetermined price. Usually, when a company grants stock options, the predetermined price refers to a future price, and the future price is usually higher than the current price. For example, if your stock is trading at around $20/share, you might get 1000 options with a strike price of $22/share. No one would exercise their options (or buy this stock) right away, because why would you want to pay $22 for the stock when you can get it for $20? But, if the stock goes up to $30, then you get a good deal when you exercise your options: you get to buy those same shares at a discount, for $22/share.
In the stock options backdating scandal, companies looked at their stocks' historical prices, found the low point, and granted options based on that date. Since the stock had gone up since then (i.e., the stock is no longer at the low point), this backdating automatically guaranteed these employees made money. In other words, say that the company stock is trading around $20 today and has been at that level for a while, but a year ago it dropped--just for a day--to $15 before rising back to $20 the next day. If your company illegally backdated stock options, it would grant options today for $15, but backdate them to make it look like the options were granted before the temporary drop. That way, employees could take advantage of the stocks' gain from $15 to $20.
This backdating, while profitable, is illegal because options aren't meant to be a guarantee of profits but an incentive to work hard to improve the company and, hence, its stock price. Backdating is cheating, making it look like stock options were granted in the past by changing the date.