nandeyanen

In Japanese, nandeyanen なんでやねん, meaning literally "why is [it]," is a phrase popularly associated with tsukkomi ツッコミ, the act of "retorting" and the comedian doing retorts in manzai 漫才, a type of comedy done by a duo where one says something stupid (the boke ボケ), while the other "retorts" by saying they're wrong or questioning them, sometimes physically hitting them, e.g. with a backhand slap on their chest.

Left: Buddha, ブッダ
Right: Jesus, イエス
Manga: Saint☆Oniisan, 聖☆おにいさん (Chapter 4, 初舞台)

Context: Jesus doing a tsukkomi on Buddha.
nandeyanen!
なんでやねん！
Why is [that]!

This phrase is in Kansai 関西 dialect, and Kansai is associated with manzai, so one can guess its popularity is due to manzai comedians from Kansai using it.

Meaning

The phrase nandeyanen is composed by three words:

nande
なんで
Why.
- nani 何, "what," fused with the de で particle that indicates, among other things, the reason for something to occur.
ya
や
Is. To be.
- Synonymous with the da だ predicative copula in standard Japanese.
- nande ya
  なんでや
  (...same as...)
- nande da
  なんでだ
  [It] is why?
  What's the reason for this?
  Why did this happen?
  Why would that be?
nen
ねん
(sentence ending particle.)
- Translates to no da のだ in standard dialect.^{(全国方言辞典:ねん)}
- nande ya nen = nande da no da, except that no の is treated like a noun in this case, and da だ becomes na な prenominally, so:
- nande na no da
  なんでなのだ
  Why is [it]?
- nande nanda
  なんでなんだ
  (contraction of the above.)

In spite of the above, it seems the phrase's meaning is closer to nande da yo なんでだよ instead, with the yo よ particle being used to call the boke's attention, given that nande nanda is unusual. The synonymous phrase naze nanda なぜなんだ is more common.

Outside of Kansai, specially in manga and anime, the phrase is often used in reference to manzai and tsukkomi. For reference, some examples:

ちょっと「なんでやねん」ってつっこんで！え･･･？なんでやねん･･･ガタガターーぐはーーっこれくらいハデに受けた方がいいかな？なんでやねん

Manga: Azumanga Daioh あずまんが大王 (Volume 1, Page 29, 負けるもんか))

Context: a boke trains receiving a backhand slap tsukkomi in preparation to meeting an Osakan.
chotto "nandeyanen" tte tsukkonde!
ちょっと「なんでやねん」ってつっこんで！
[Try] doing a tsukkomi [saying] "why"!
- 「」 - quotation marks.
e...?
え･･･？
Eh...?
nandeyanen...
なんでやねん･･･
Why...
gata gataaa
ガタガターー
*sound of chairs and desks falling*
(onomatopoeia.)
guhaaa'
ぐはーーっ
Aaargh!!
{kore kurai hade ni uketa} hou ga ii ka na?
これくらいハデに受けた方がいいかな？
[Do you think] [it] would be better if [I] received [the tsukkomi] [reacting] this much showy? (literally.)
- hade
  派手
  Showy. Gaudy.
- Do you think I should react this extravagantly?
nandeyanen
なんでやねん
Why.