Your child theme must have its own style.css file; it’s required in order to work.
As @andrewmills kindly pointed out, in order to use a child theme, and in fact any theme, you need a stylsheet. In a child theme, this is used to import the styles from the parent theme. It’s also where you’d make any modifications to override the default styles.
I asked because it seems odd to me to provide an easy way within the theme to make changes to the CSS when the only way for these changes to be update-proof is within a child theme. This theme is not alone in this and I can’t help but wonder how many people get tripped up by the practice.
Appearance > Edit CSS
That looks like custom CSS added from JetPack – in which case, those changes are fine – they won’t be overwritten by a theme update.
If you are editing the theme’s style.css file, that will get overwritten.
As @wpyogi pointed out, the reason you’re seeing an Appearance > Edit CSS menu option is because you have Jetpack installed and have enabled that option. This is an extra feature added by that plugin. It’s not due to the theme itself.
You can find out more on that Jetpack feature, here…
http://jetpack.me/support/custom-css/
Thanks, I hadn’t figured out the Jetpack connection. This explains why I see it on one site but not another!
