Manufacturers typically plan their aircraft production well into the future, which includes having a buyer lined up for each aircraft, so they will know their position in the production line and have an anticipated date for delivery.
An order means that the buyer has agreed to purchase a certain aircraft in the production line, at a certain price. The buyer may cancel, but there will probably be a substantial penalty for doing so.
An option means that the manufacturer has reserved a certain aircraft in the production line for the buyer, usually at a certain price. However, the buyer will make the decision on whether to convert this to an "order" at a later date. There is less commitment than with an "order".
A purchase option is even less of a commitment than an "option." This just means that the buyer has agreed to purchase aircraft at a certain price, but it's not tied to a specific aircraft at that time.
It is becoming more common for buyers to mix these three types of orders, which allows them to have a balance of locking in an aircraft and price with orders, and less risk and commitment with options and purchase options.
These can all be canceled, though of course there will be more penalties for breaking a more firm commitment. Buyers may also change their order, either for their own or the manufacturer's business reasons.
The detailed finances of how much is actually paid for aircraft, and how much it costs to make or break any of these contracts, is generally not disclosed. Negotiations can be very specific to each order. For a rough estimate, this book considers that for 6 aircraft worth 45 million per unit, options would be worth 2.3 million each to the airline, or about 5%. This book estimates the down payment on a firm order at 10 to 15 percent, but notes that at least in the case of business and commuter aircraft, depending on market conditions, this may not always be required.