Definition:
Option holders have the right, but not the obligation, to buy or sell the underlying instrument at a specified price(strike price) on or before a specified date(exercise date) in the future. (this is different for European options as they can only be exercised at the end date). Exercising the option is using that right to to buy or sell the underlying instrument.
Example
Let’s say we wish to exercise 20 AAPL october 20th call options which have a strike price of 100$. We would let our broker know and he would then “use up” your option contract (hence it no longer has any value) and buy 20 * 100 (each option contract is for 100 shares) 2000 shares of AAPL at a price of 100$. This also means you have to have the money to be able to buy 2000 shares at 100$ = 200,000$. If AAPL is at 105$ you would then earn 10,000$ profit on this trade.
Brokers will often times allow you to simply take the profit as well just like you would at expiry by immediately selling the shares. Hence in the example above you would just obtain 10,000$ instead of needing the 200,000$ cash to have to purchase the stocks in the interim.
More Information
In general it is wise to avoid exercising options as you lose the time value of your option. This is not always the case and can be useful if you spot arbitrage opportunities. Traders can also take advantage of early exercise before dividend dates and other considerations.
On this simulator you can exercise options by finding the option you want on your Open Positions page and clicking “Exercise”.