When a camera has a button that says 'scene'?

That means that you are able to select like: potrait, marco, fast action, blur reduction, mountain, sunset set, candle, night potriat, etc
I just want to make sure. Like, look at his camera: http://www.amazon.com/...0034XIMG4/

And looking at the back picture, where it says 'scene' with the blue camera button, that means you can select all of those ^^^^ right?

Yes

I have a Nikon, and this is what "scene" means, i.e. Preset settings for specific scenarios.

Yes an L110 will have all those so don't worry, no actual learning will be involved.

On cameras that have a lot of manual control, people who like to tinker with manual controls may rarely use the Scene settings. However, with cameras like the Nikon L110 that lack the direct manual controls, the scenes can often make a smarter automatic choice than the general purpose Auto setting.