Disclaimer: I am not a financial advisor. This is mostly a summary of what I learned on the internet for me to refer to in the future. Options can blow up your account if you're not careful. Do not yolo your retirement money and end up like the people on /r/wallstreetbets.
Options can be used as insurance for your positions (ex. in case of a stock market crash) for less degenerate investors, or a leveraged bet (ex. an all or nothing bet to 10x your money or lose it all) for more degenerate "investors."
Options can be described by four properties
For example, a call option on the stock $MEME that expires June 9th at a strike price of $420 could be written
MEME 6/9 420c
The price of the option is called the premium, just like the premium you pay for insurance.
A call is a bet that a stock (or whatever your underlying) will go up.
For a stock $MEME, a call option with a strike price of $420 means that the option price at expiration would increase by $100 for every dollar $MEME goes over $420.
However, if $MEME is $420 or less on expiration, the call option would be worth $0.
$MEME call price at expiration = 100 * ($MEME price at expiration - strike price)
or $0 if $MEME price is less than or equal to the strike price
The option price at expiration is the intrinsic value of the option. It's based entirely on the difference between the price of the stock and the strike price.
If the intrinsic value of the stock is positive, or the price of the stock is greater than the strike price (i.e. $MEME is worth more than $420, the strike price), then the option is said to be in-the-money (ITM).