As @Riateche correctly pointed out, "чё" is a slang word for "что" - meaning "what". "Вон" (in this context) means "that" or "there" (similarly, "вот" for "this" or "here").
There are two - somewhat different - meanings this phrase can take.
It is used to express an understanding of something at last, i.e. if somebody couldn't understand something for a while and then finally it dawned on them, it would be the right time to use it. The English equivalent would be "That's what it is!"
Consider this dialogue:
– Не понимаю, нафига тебе нужна эта штуковина?
– Эта штуковина - это ключ от замка на моём сарае.
– Вон оно че!
with its English equivalent:
– I don't get it, what the heck do you need this thing for?
– This thing is the key from the lock on my shed.
– That's what it is!
Here, the meaning of "вон/вот" is "that/this". In its second meaning, "вон/вот" is used as "there/here" and means, literally, "here's what" or "here's the thing"/"here's the deal". It would be used to express a level of certainty or authority at the start of a speech, for example:
Вот оно чего Михалыч! Выйдешь ты сейчас в цех, а меня нет, ни у станка, ни в столовой, даже в Челябинске меня нет.
Here's the deal, Mikhalych! You'll come out now onto the machine floor - and I'm not there, not near the workbench, not in the canteen, not even in Chelyabinks.
Вот оно че Михалыч, мне давеча сон про тебя приснился. Идешь ты значит по цеху в красных труселях, все по сторонам оглядываешься
Here's what [it is], Mikhalych, I saw a dream about you the other day. You're walking along the machine floor in your red underpants and looking around.