Layer transparency

Hi, how do you create a new layer that is transparent (i.e. has a grey and white checkerboard icon in the layers panel)? I opened up a new document, selected "Background Contents" as "Transparent" but when I click "New Layer", the icon is white, not checkerboard. I'm following a tutorial and the tutorial version appears checked while mine isn't so I'd just like to understand where we are diverging. Googling transparency in Photoshop just throws up a whole load of technical jargon I'm too much of a noob to understand!

I'd be really grateful if anyone can explain why new layers in my document aren't transparent.

Many thanks