なぜなら + から

When combined with the conjunction particle から, なぜなら (or なぜならば) forms a set pattern that can be translated as 'why (A), that is because (B)'. Essentially, it is a way to highlight that a 'because' is coming at the end of the sentence, drawing attention to it.
なぜなら itself is a conjunction that is a combination of the adverb, なぜ 'why', and the hypothetical form of だ, なら. Literally, なぜなら～から is similar to 'why is (A) so, (B) is the cause'. This sounds quite dramatic in English, but is a perfectly natural way of emphasizing a statement/fact in Japanese.
To use なぜなら～から, state that fact/important piece of information as (A). Then, at the beginning of a new sentence, なぜなら will be followed by the reason/cause, with から finishing the sentence.

• 明日(あした)は仕事(しごと)に来(き)ません。なぜなら、明日(あした)は友達(ともだち)の結婚式(けっこんしき)に行(い)くからです。
  I will not come to work tomorrow. Why? That's because I will be going to my friends' wedding.
• 卵(たまご)を使(つか)わないで作(つく)ってください。なぜなら、私(わたし)は卵(たまご)アレルギーだからです。
  Please make it without using eggs. Why? Because I'm allergic to them.

The primary function of なぜなら in Japanese (as opposed to simply using から or ので by itself) is to gain the attention of the listener, and inform them that important information is coming.