Can someone please help me understand how stock options work? And what does vested stock options means?

Stock options given by companies usually allow you to buy the stock at the price mentioned in the options, if you choose to exercise it before the the expiry date. Typically the price will be lower than the market price.

By vesting, it means that the batch of stock options given will be distributed equally over the period of time mentioned i.e. 100 stock options are given to you over 5 years meaning 20 stock options are vested to you each interval e.g. year 1, year 2 etc. Usually it serves as a retention mechanism. The longer you stay in the company, the more options that are vested.

There are also restricted stock units that some companies offer. That is different from stock options. These are actual stocks that are vested over the period of time.

Forgot to add that these are all income taxable too.