There are several Concession Card types. Not all Concession card types provide all kinds of discounts.

The main advantage of Health Care Cards is that they provide discounts when you buy prescription medicines, which are on the PBS. If you do not have a Health Care Card, you pay up to $36 (I am not sure about the exact figure, but it is something close to $36). If you have a Health Care Card and present it to the chemist/pharmacist when you buy a medicine, the maximum amount you pay is only $6.50, instead of $36. These numbers are not exact numbers and they usually change every year.

Some other organisations, e.g. utility and transportation companies, might provide you with a discount if you carry a Health Care Card. You might need to call them to ask if they provide discounts for Health Care Card holders. 

If you live in NSW... 

The following link provides a list of 40 different ways, which the NSW government provides to ease the cost of living for NSW residents. The list includes savings in the following areas. 

• Car Registration & Licensing
• Electricity, Water & Gas
• Public Transportation
• Health
• Children
• Recreation & Leisure
• Education

and more... 

Check out the official website: https://www.service.nsw.gov.au/campaign/cost-living

The most common Concession cards are (1) Health Care cards, and (2) Pensioner Concession cards. They are usually issued automatically by Centrelink to families/individuals, who have low income. For more information about your eligibility for concession cards, please check the Centrelink website:

https://www.humanservices.gov.au/individuals/services/centrelink/pensioner-concession-card

https://www.humanservices.gov.au/individuals/services/centrelink/health-care-card