別

1. "Separate." Kokubetsu, for instance, means "separated by country" (that is, if you took a group of people or things and separated them into groups by country of origin).
2. "Special," "especially." In this sense, betsu is like a shortened version of tokubetsu, the usual dictionary gloss for "special." (You can also isolate toku in a similar way.) To make betsu into the adverb "especially," you append a ni. Betsu ni nai, often contracted to betsu ni, means "nothing in particular."
3. "Another." This meaning comes from adding a no to the end. Betsu no sekicho would be "another sekicho," whereas betsu ni sekicho would be "especially sekicho." It's a lot less confusing in hiragana, trust me.
4. "Other than." This meaning is formed by stating the differentiated thing as the topic of the sentence (using a wa particle), appending a betsu ni shite to it, and then finishing the thought. Everything2 wa betsu ni shite, intaanetto wa tsumaranai tokoro da would mean "Everything2 aside, the internet is a boring place."