Deborah, in the Hebrew, means 'the bee', in the sense of orderly motion from its systematic instincts. The root word is dabar, which means, 'to arrange'; used figuratively of words, 'to speak'.
Debra is a good alternate spelling of the name, but it exists only as a Greco-Roman alteration. The ending -ah on Deborah is typical of feminine names in Hebrew as it often denotes a word's femininity. For example, Sarah, Hannah, Oholibamah, Hadassah, etc. Are all feminine names, and in some cases, feminine words.