Flower Background Effect

In anime, sometimes flowers are used as a background effect symbolizing that a character is peaceful, happy-go-lucky, carefree, easy-going, specially if they're in love, thinking about romantic things, or if they have a gentle, fuzzy personality.

Karuta Roromiya 髏々宮カルタ, example of flower background, overly long sleeves (moe-sode 萌え袖).

Character: Karuta Roromiya 髏々宮カルタ
Anime: Inu x Boku SS, 妖狐×僕ＳＳ (Episode 9, Stitch)

Meaning

Most likely, this flowery visual language comes from one of the following Japanese expressions:

{mawari ni ohana ga tonde-iru} hito
周りにお花が飛んでいる人
Someone [who] {flowers float around}.
- tobu
  飛ぶ
  To jump. To fly. To float. (to not be in contact with the floor.)
- Literally this background effect, with flowers drawn floating around characters.
- Meaning that someone is calm, gentle, fluffy, has a warm, comforting personality.^{(chiebukuro.yahoo.co.jp:周りに花が飛んでる人)}
- In anime, such characters tend to talk slow and, well, think slow sometimes. They're also likely to be drawn with sweat drops flying away from them when they feel nervous.
atama no naka ga ohana-batake
頭の中がお花畑
Inside [one's] head is a flower field.
- Meaning that someone's mentality is extremely peaceful, like one of those peaceful flower fields, with a gentle breeze making the flowers calmly swing.
- Used when someone is in very high humor, like when they've fallen in love, thinking about things romantically in general, or, like the above, when they have a gentle personality.
atama ni ohana ga saite-iru
頭にお花が咲いている
A flower is blooming on [someone's] head.
- Another way to say the inside of their head is a flower field.^{(detail.chiebukuro.yahoo.co.jp:頭に花が咲いている)}

Examples

For reference, some examples of flowers in the background:

Harpy, ハーピィ, wearing overly long sleeves (moe-sode 萌え袖) that are also detached sleeves, デタッチドスリーブ, with flowers in the background.

Character: Harpy, ハーピィ
Anime: Maoujou de Oyasumi 魔王城でおやすみ (Episode 5)

Context: Harpy is a monster girl that loves girls' talk, including talking about love and romance. She has wings, feather ears (hanemimi 羽耳) and uncute claws that she hides with detached overly long sleeves (moe-sode 萌え袖).

Manga: Mairimashita! Iruma-kun 魔入りました！入間くん (Chapter 54, 正反対の入間)

Context: Suzuki Iruma 鈴木入間 suddenly changes personality, from gentle to edgy, and his classmates talk about it.
{itsu-mo wa ohana ga tonderu kedo...
ima wa kuroi hane ga matteru} kanji?
いつもはお花がとんでるけど･･･
今は黒い羽が舞ってる感じ？
[Like] {usually [there are] flowers floating [around him],
but now [there are] black feathers fluttering [around him]}?
(contrastive wa は.)
- mau
  舞う
  To dance.
  To flutter on air.
aa
あー
Yeah.
wakaruu
わかるー
[I] know~. (in the sense of "I agree," "I get what you're saying.")

Maaka Karin 真紅果林 has a flower-shaped nosebleed.

Character: Maaka Karin 真紅果林
Anime: Karin かりん (Episode 1)

Context: Karin is a reverse vampire, who produces extra blood instead of sucking it, which she expels in the form of explosive nosebleeds, which in anime is often associated with being perverted and lewd.
This series is a romantic comedy, and she got the urge expel blood when she was next to a guy.
Here, Karin's nosebleed is drawn like red flowers, implying her blood (what's inside her head) is a bunch of flowers, and that she's in love with that guy.

Character: Takahashi Misaki 高橋美咲
Anime: Junjou Romantica, 純情ロマンチカ (Episode 12)

Context: Takahashi Misaki practices what to say.
kyou wa tsukareteiru to omou kara
今日は疲れていると思うから
[I] think that [you] are tired today, so.
mazu wa ofuro ni suru?
まずはお風呂にする？
[What do you want to do] first?
Bath?
gohan ni suru?
ご飯にする？
Dinner?
soretomo... ore?
それとも･･･俺？
Or... me?
- This is a trope called shinkon-santaku 新婚三択, "newly-wed three choices," in which typically a wife welcomes her husband by giving him three choices that end up "or me," although variations exist.

For reference, some related symbology.

Shinomiya Kaguya 四宮かぐや with a flower sprouting out of her head.

Character: Shinomiya Kaguya 四宮かぐや
Anime: Kaguya-sama wa Kokurasetai? ~Tensai-Tachi no Ren'ai Zunousen~ かぐや様は告らせたい？～天才たちの恋愛頭脳戦～ (Season 2) (Episode 2)

Context: a flower sprouting of someone's head is another symbol for having one's head full of flowers, in love. Sometimes, it's used to mean they're being silly, funny.

An example of "lilies," yuri 百合, used as a visual pun for lesbian romance.

Left: Moritani Hiyori 森谷ヒヨリ
Right: Kotoura Haruka 琴浦春香
Anime: Kotoura-san 琴浦さん (Episode 5, Censored)

Context: lilies are used as background effect in scenes featuring lesbian romance in anime because yuri 百合, "lily," is a term for lesbian fiction.

Example of BL shipping Harry Potter and Neville Longbottom.

Left: Neville Longbottom
Right: Harry Potter
Anime: Asobi Asobase あそびあそばせ (Episode 4)

Context: roses are used background effect in scenes featuring gay romance in anime most likely because bara 薔薇, "rose," is a term for gay fiction.