New Year's Decoration

Every year around New Year's, I see odd decorations being sold at the grocery stores. Here's one of them.

It's called a "kagami-mochi." In my head, the translation comes out to "mirror-rice-cake." That sure doesn't make any sense, so my brain is most likely misunderstanding something. But every year, instead of bothering to find out the meaning behind these decorations, I keep wondering what meaning they must hold.

So this kagami-mochi, it has two layers of rice cake, with an orange on top. Sometimes, I think it also has dried persimmons on the top too. There's a ribbon in the shape of a crane around the rice cake.

This one is a bit fancy I guess, because it has a fan at the very top, leaves and paper hanging in front.

So what's my guess as to what this means? Hmm. I think I once heard someone explaining that you to let the rice cake dry out and crack, then put it into a special New Year's soup to drink and it's supposed to bring good luck for the year. If the rice cake doesn't dry out and crack and you use a knife to cut the rice cake, then it's bad luck or something.