It is a Phalaenopsis Orchid and the flowers have died, perhaps through old age or unsuitable growing conditions. With care it might flower again.

I have put the American Orchid Society culture notes in the link. There are also many past Phalenopsis threads on this site . Put Phalaenopsis in the search box to find them.

AOS Phalaenopsis notes

Thank you! All the flowers have fallen off now :( Do you think I should re-pot it?

I am of the school of doing as little as possible......it depends on what sort of growing conditions you can provide wherever you are in the USA. The condition of the plant and the roots. The number of drainage holes at the base of the pot, and even what sort of horticultural knowledge you have.....Some posters here have never grown anything and yet they are told to do major "surgery" on a first time plant, when maybe better advice would be to try and get growing experience by sitting back and observing.

The ice orchid thing is a gimmick to prevent overwatering. There are many past emotional threads you can read on that subject.

Anyway, tell the posters here more about the growing conditions you can provide, your state code or climate zone, temperatures, light from windows and the potting material in the pot which is probably sphagnum moss.

I'm located in NY. It's standing at a table close to the window, so it gets light but not direct sunlight. We keep the apartment at about 75 degrees. I already read about the ice controversy and will start watering it normally instead of using ice. It looks like it is planted in moss (although I am not sure - not an expert). There are three drainage holes on the bottom of the small plastic container it came in. The leaves look like they are in good condition.

It all sounds positive, follow the AOS notes and use a complete fertilizer with trace elements (Something like Miracle-Gro all purpose fertiliser with trace elements) read up on the watering routine needed for spag, where you have to let the medium dry a little bit between waterings.

Find some more notes on the net that are written for Northern USA.

Sit back and observe and hopefully the plant will grow some new roots if it is happy.