A garden centre is typically a shop which sells a range of garden supplies. You may also hear it being called a nursery.
Garden centres range in size and supplies. There are some small garden centres attached to large shopping stores which tend to have basic range of supplies, whereas there are large stores which are dedicated to gardening so you should be able to get most of the things you need to have make a beautiful garden at home, such as pots and plants, seeds, seedlings, compost and fertilisers
Many garden stores are so big you won't miss them! Some garden supply stores may be attached to a larger store such as Big W or K Mart. Every Bunnings Warehouse tends to have a large nursery attached to it with large trolleys which you can use to buy large pots and soil. If you are looking for a specific garden centre near you, check out Local Business Guide to look for niche businesses in your local area.
It does pay to do some research prior to attending a garden centre. If you are landscaping a backyard you may want to involve a landscaper or read up on what kinds of flowers or plants you would like to plant in your backyard, as it is harder to remove plants once they are established! You may find that you want to focus on a vegetable garden, or you may be more interested in planting flowers and create a beautiful masterpiece.
There are some local nurseries which offer groups and classes to learn more about how to garden with lots of tips and tricks to create a beautiful garden.