These are very common spiders around Sydney, and throughout eastern Australia. They're named for the pattern they weave into their webs:
St Andrew's Cross Spiders are named for their bright web decorations - zig-zag ribbons of bluish-white silk that form a full or partial cross through the centre of the orb web.
I don't know who gave it the name "St. Andrew's Cross"; although you can see why it got the name. As you can see in the photo, these spiders arrange their legs in pairs, so it almost looks like they have four, and they commonly position themselves in the center of their webs, holding their legs aligned with the white cross in their webs. Which is just cool.
As with most spider species, female St. Andrew's Cross spiders are larger and more colorful than the males. This one, which I came across in Ku-ring-gai Chase National Park, is the largest one I've seen. She seems to have been a bit lazy, as only one leg of the cross is present.
Scientific name: Argiope keyserlingi, in honor of German arachnologist Eugene von Keyserling.