This post is meant to be a landing page for a topic in the pinned Welcome post. At some point it will be locked, but feel free to add suggestions for edits in the meantime.
For purposes of this discussion, we'll be focused on American style equity options. An option is a limited duration contract between a buyer and a seller. It confers certain rights to the buyer and obligations to the seller.
Options have a deliverable, a strike price, a premium, and an expiration date. An option contract generally represents control of 100 shares of a particular stock or ETF (this can be modified in certain circumstances, such as if the stock splits or offers a special dividend, but for now we'll focus on the rule rather than the exception). The strike price is the cost per share that will be exchanged if the contract is exercised. The premium is the amount paid by the buyer and received by the seller in order to enter the contract. The expiration date is the date after which the contract between buyer and seller no longer exists.
Options come in two flavors: Calls and Puts. A call option gives the buyer the right to buy shares of an underlying, and obligates the seller to deliver those shares. A put option gives the buyer the right to sell shares of an underlying, and obligates the seller to take delivery of those shares.
An underlying can be an individual equity, such as as AAPL or MSFT, or it can be an ETF, such as SPY or KRE. Not all tickers have options, usually only the most actively traded will have them available.
So let's put these concepts together. It's June 1st and Bob has done some analysis of XYZ company, which is currently trading on the NYSE for $100. He believes that the stock is undervalued and there could be a big increase in price in the near term, but he would like the opportunity to buy the shares at $100 if that happens. Bob decides to buy a call option expiring in 30 days. The call option has a strike price of $100 and an expiration date of June 30th. Bob will need to pay a premium to buy this contract, and he sees that the option is currently trading for a bid of 4.90 and an ask of 5.10. Bob submits a bid to buy the contract at the middle price of 5.00 between the current bid and ask. The option premium is per share, and since the contract represents 100 shares, Bob would need to pay $500 in total for this contract.
If a seller agrees to Bob's price, then Bob will have the right to purchase those shares on or before June 30th for $100 each. If XYZ goes up to $110 by June 30th, then Bob could decide to exercise his right to buy the shares. Bob's total cost for the shares, then, is $100 per share plus the $5.00 per share he paid for the right to buy them. ($100 + $5) X 100 = $10,500. Bob's average cost per share is $105. $10,500 / 100 = $105. Since XYZ is now trading at $110 and Bob only paid $105, he has made a profit. He can sell all or some of the shares for an immediate gain of $5 per share.
Let's say Bob decided to hold on to those shares of XYZ because he thought it would keep going up. Sure enough, it's soon trading at $125. But Bob is worried about some stuff going on in the world and would like to make sure that he can still make a profit from his shares if the market starts to sell off. It's August 1st and Bob buys a put contract with a strike price of $120 expiring in 60 days. Bob pays a premium of $5 for this contract. If XYZ falls below $120 on or before August 30th, Bob can exercise his right to sell his shares for $120 per share. On August 30th, XYZ is trading for $95. Bob exercises his contract and collects $12,000 ($120 X 100 shares). Bob paid $500 for this contract ($5 X 100 shares), so his net sales price is $11,500, or $115 per share.
What would happen if XYZ had been trading at $130 instead of $95? Well, Bob wouldn't want to sell his shares for $120 if he can sell them for $130 on the open market, so the contract would expire worthless. Bob still had to pay $5 per share for this contract, so he loses that premium.