As I stated in my comment, options are futures, but with the twist that you're allowed to say no to the agreed-on transaction; if the market offers you a better deal on whatever you had contracted to buy or sell, you have the option of simply letting it expire.
Options therefore are the insurance policy of the free market. You negotiate a future price (actually you usually take what you can get if you're an individual investor; the institutional fund managers get to negotiate because they're moving billions around every day), then you pay the other guy up front for the right of refusal later. How much you pay depends on how likely the person giving you this option is to have to make good on it; if your position looks like a sure thing, an option's going to be very expensive (and if it's such a sure thing, you should just make your move on the spot market; it's thus useful to track futures prices to see where the various big players are predicting that your portfolio will move).
A put option, which is an option for you to sell something at a future price, is a hedge against loss of value of your portfolio. You can take one out on any single item in your portfolio, or against a portion or even your entire portfolio. If the stock loses value such that the contract price is better than the market price as of the delivery date of the contract, you execute the option; otherwise, you let it expire.
A call option, which is an option to buy something at a future price, is a hedge against rising costs. The rough analog is a "pre-order" in retail (but more like a "holding fee"). They're unusual in portfolio management but can be useful when moving money around in more complex ways. Basically, if you need to guarantee that you will not pay more than a certain per-share price to buy something in the future, you buy a call option. If the spot price as of the delivery date is less than the contract price, you buy from the market and ignore the contract, while if prices have soared, you exercise it and get the lower contract price. Stock options, offered as benefits in many companies, are a specific form of call option with very generous terms for whomever holds them.
A swaption, basically a put and a call rolled into one, allows you to trade something for something else. Call it the free market's "exchange policy". For a price, if a security you currently hold loses value, you can exchange it for something else that you predicted would become more valuable at the same time. One example might be airline stocks and crude oil; when crude spikes, airline stocks generally suffer, and you can take advantage of this, if it happens, with a swaption to sell your airline stocks for crude oil certificates. There are many such closely-related inverse positions in the market, such as between various currencies, between stocks and commodities (gold is inversely related to pretty much everything else), and even straight-up cash-for-bad-debt arrangements (credit-default swaps, which we heard so much about in 2008).