Sometimes "very" used to mean "exactly", but this is not a common usage. That is, you can't replace "exactly" with "very" in any sentence. Look for other examples before using it. As well as "(it is) the very thing (etc...)", it's also used in these examples: "I have found it, right under my very nose!" (=it was in the most obvious place: figuratively, "exactly under your nose") "There it is, in the very place where I had left it." (=the exact place)

= exactly the thing you are looking for

Exactly what is needed or wanted. http://dictionary.reference.com/browse/very+thing,+the