Answer: Your palm is playing host to some insects - mealybugs or scales, probably. These pests feed by attaching themselves to the stems and sucking the fluids from the tissues of the plant. They exude a sticky substance called honeydew and the honeydew is what you're finding on the leaves and on your floor. Once you get rid of the pests, the honeydew problem will no longer exist. You'll need to carefully examine your plant, looking for the pests. Once you determine which it is, you can use a chemical control - or you can painstakingly pluck each pest from the plant with tweezers.
Best wishes with your palm!
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