This page explains the five basic characteristics which define every option contract:
Underlying Asset
Option is a derivative security, a contract giving the owner (buyer) of the option the right (but not the obligation) to buy or sell a defined quantity of a defined asset. This asset is called underlying asset (or underlying security or just underlying).
The use and popularity of options has expanded in the last decades. Nowadays there is a wide range of underlying assets for which options exist. Among the most widely known are options on single stocks (shares in companies traded in the stock market).
There are also options on indices such as the S&P500 or the VIX (volatility index). You can also trade options on futures, bonds, interest rates, currencies, ETFs, and many other kinds of assets or economic variables.
Call Option vs. Put Option
There are two basic types of options, call options and put options. A call option gives its owner a right to buy the underlying asset, while a put option gives its owner a right to sell the underlying asset.
Strike Price
Strike price is the price for which the option's owner can buy or sell the underlying security, if he decides to exercise the option.
An option's strike price is fixed and does not change during the whole life of the option. For one underlying and one type of options (calls or puts) there are usually at least several different strike prices available. For example for a stock which currently trades at 57 you can trade call options with strike prices of 50, 55, 60, 65 etc. and put options with strikes of 50, 55, 60, 65 etc. But of course every single option always has only one strike price defined and once you own it you can't change its strike – it's fixed.
Remember that an option's strike price is a different thing than an option's market price. Option's market price (also called premium) is the price for which you trade the option itself and it changes during the life of the option, depending on supply and demand in the options market.
Expiration Date
Options have limited life. Every option has a defined expiration date, which is also fixed during its whole life and nothing can change or move it. If an option is not exercised before or on its expiration date, it becomes worthless (it expires) after that date.
American vs. European
The distinction between American and European options is about when an option's owner can exercise the option. An American option can be exercised during its whole life, this means from the moment you buy it till the moment it expires (its expiration date). On the contrary, a European option can be exercised only at one single moment – the moment when it is expiring.
This has nothing to do with the trading in both types of options. You can buy or sell American, as well as European options, any time during their life (when the options exchange is open if the option is exchange traded).
Remember that these terms are not related to geography in any way. Both types of options trade in many places in the world.
What All Have in Common
There is one important thing all these five characteristics of every option have in common: they are all fixed. None of them can under any circumstances change for that single option during its whole life.
When buying an option, you know its underlying asset, whether it is a call or put, its strike price, expiration date, and whether it is an American or a European option. You can be sure these characteristics will stay as they are for the whole time you will be holding the option.