An octopus card is your ticket around the city.
Public transportation wise you can use it for pretty much anything besides taxis. It is a small card, not unlike a credit card, that you add money to.
This money will pay for your fairs on trams, trains, buses, ferries, MTR, and minibuses.
At least for MTR fair it also costs a couple HKD less to pay with octopus card rather than single ticket journey cards.
BUT THAT'S NOT ALL
It is true that for the most part I use my octopus card to pay for my transportation, but you can also use it in some shops (most notably 7/11 and grocery stores).
Octopus card is super useful and I have it with me all the time.
It will cost you HKD150 to start with, but that includes HKD100 already added on your account. You can get back the HKD50 deposit if you return the card when you are done in Hong Kong.
Overall? octopus cards are super useful and should be one of the first things you get when you arrive in Hong Kong.
Do you have questions about life in Hong Kong? Post a comment and I'll do my best to answer your question