It is an orchid, a Phalaenopsis. The "stems" you are talking about are flower spikes. Once the flowers die, these spikes dry up, it does not mean your orchid is dying. You can cut them off and your orchid should produce new spikes in time.
It does seem you are not watering enough, though, the roots on top look shriveled. It looks like there is a clear plastic pot inside the decorative pot? Take the plastic pot out and check the roots, they should be plump and either green (wet) or silvery (dry), if they are brown and shriveled you aren't watering enough, if they are brown and mushy, you are watering too much (I suspect the former). When you water, water thoroughly NOT just a little bit. Then water again as the bark is just nearing dryness. It may also need a repot. Check out the thread "The Phal abuse stops here" it is a good one for new orchid owners!
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