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The price that you paid for the option gives you "the right but not the obligation" to buy shares at the exercise price at any time up until the date that the option expires.
There are two components to an options value:-

- the extrinsic value. ( The time component); &
- the intrinsic value ( the amount by which the ESR share price exceeds the Exercise Price of the option)

For ESRO the expiry date is 27 June 2021 and the exercise price is $0.05.

Theoretically, you would exercise your options "on but before close of market on 27 June" if the ESR share price was greater than $0.05. (They are however able to be exercised at any time between the date they are purchased and the expiry date. Options with this feature are called "American options" )

By exercising on 27 June 2021 you maximise the extrinsic value of the options (fancy way of saying the time value associated with the option purchase).

If you don't exercise the options before close of market on 27 June, they lapse and are worthless.

The amount that you would pay to exercise is the number options held x the exercise price.

Theoretically you would not exercise the options if the share price is below the Exercise price of $0.05 at the time of exercise.