The nature strip is the piece of land between the footpath and the road, or between your house and the road. Most of the time you don’t actually own this piece of land and it belongs to the local council.
This means you need to consult your local council’s rules first. You can’t usually touch the street trees, you may need a permit, or have to stick to a limited range of permitted plants. However there is a growing trend and acceptance of nature-strip planting from councils across Melbourne, allowing the possibility of replacing boring old grass with something the whole neighbourhood can admire and enjoy.