This has always confused me. Dictionary.com doesn't help at all. Candy and meat just don't go together that well.
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The key is that meat used to just mean "food". The first entry under meat at Merriam-Webster has exactly that definition, though of course the primary sense of meat today is definition #2, which specifically refers to animal flesh. However, the older, broader sense of "meat" still sticks around here and there, such as the practice of referring to the edible part of a nut as the "meat", and in compounds such as "sweetmeat".
The OED reports the following definitions for meat (I report the first two):