Realization Mark

In manga and anime, when a character realizes something, notices something, is surprised by something, or has their attention directed at something, a mark is drawn banging away from their head or eye to symbolize their sudden realization.

The exact mark varies. It can be an impact mark, three or more lines, a flash, or a lightning flash, depending on the style and situation.

Anime: Bokutachi wa Benkyou ga Dekinai ぼくたちは勉強ができない (Episode 1)

• Impact Mark
• Lines
• Flash
• Lightning Flash

Impact Mark

A crown-like mark banging away from the character head is used when they notice something, realize something, or are surprised by something.

• ki-dzuku
  気づく
  To notice. To realize.
• mitsukeru
  見つける
  To find. (something by seeing it.)
• odoroku
  驚く
  To be surprised.

You could also say they look like ∑, the Greek letter "sigma."

It could be they found something they weren't aware of, or something just said something they weren't expecting.

Anime: Ouran High School Host Club, Ouran Koukou Hosuto-Bu 桜蘭高校ホスト部 (Episode 4)

• Sweat drops are another common symbol.

Anime: Watashi, Nouryoku wa Heikinchi de tte Itta yo ne! 私、能力は平均値でって言ったよね！ (Episode 6)

• Circle eyes are another common symbol, too.

Note that this mark is used more generally whenever something springs out or pops out of somewhere.

Anime: Haiyore! Nyaruko-san 這いよれ！ニャル子さん (Episode 1)

Since it's used on the head I guess it's because the head is supposed to be moving somehow. Maybe because people turn around or twitch when they suddenly notice something.

Lines

Three or more lines can also be used to symbolize a character has noticed something.

Character: Naganohara Mio 長野原みお
Anime: Nichijou no Zero-wa 日常の０話 (Episode 0, OVA)

• konsento-me
  コンセント目
  A term for eyes drawn like vertical bars.

In this case, I guess it could be based on the character opening their eyes wide in realization. Who knows.

Anime: Excel♥Saga, エクセル♥サーガ (Episode 2)

It's also possible that this is a simplification of a flash or sparkle.

Manga: One Piece (Chapter 13, 〝宝物〟)

• Luffy ルフィ notices something.
  
• n?
  ん？
  Hmm?
  

Note that there's a type of sweat drop drawn very similarly to the realization mark. Observe the symbols below:

Manga: K-On!, Keion! けいおん！ (Volume 1, Page 30)

• Context: Hirasawa Yui 平沢唯, who started learning to play the guitar, tells her impressions about the guitar strings to Tainaka Ritsu 田井中律.
• {hosokute katai kara} yubi φ kichaisou
  細くて硬いから指切っちゃいそう
  {Because [they] are thin and hard}, [it feels like] [it] will cut [my] fingers.
  • Symbol: plewds, a type of sweat drop drawn on air.
• piin
  ピーン
  *sound effect of light turning on*
  • Symbols: realization lines and an idea light bulb.

Flash

A flash of light drawn on the background tend to be used when a character figures out something, or notices some important information. Unlike the previous marks, this one looks like the character is focused on something, probably thinking complicated stuff, and they just had a moment of clarity.

See Beta Flash for details.

Anime: Inu x Boku SS, 妖狐×僕ＳＳ (Episode 4)

• suiri
  推理
  Deduction.
• furasshu
  フラッシュ
  Flash.

Lightning Flash

A lightning flash on the background, accompanied by a thunder in anime, is used when a character is completely and figuratively shocked by something they've seen, heard, or figured out.

Anime: Gamers!, ゲーマーズ！ (Episode 6)

• shokku
  ショック
  Shock.
• inazuma
  稲妻
  Lightning flash.

In some cases, that angular lightning is combined with spark-shaped flashes.

Anime: Ore wo Suki nano wa Omae dake kayo 俺を好きなのはお前だけかよ (Episode 2)