tsurime ツリ目

In Japanese, tsurime ツリ目 means "upturned eyes," literally "fished up eyes." Broadly speaking, it's an eye shape in which the outer corner of the eye is much higher than the inner corner.

The opposite term, downturned eyes, is tareme タレ目.

Character: Shirakiin Ririchiyo 白鬼院凜々蝶
Anime: Inu x Boku SS, 妖狐×僕ＳＳ (Episode 2)

Meaning

Written with kanji, tsurime ツリ目 is tsurime 釣り目 or tsurime 吊り目. The tsuri ツリ part is the ren'youkei 連用形 of the verb, but which verb is it exactly depends on the spelling:

tsuru
釣る
To fish up. To angle. In the sense of using a fishing rod to catch a fish.
tsuru
吊る
To hang. Using a string or rope, for example.

In other words, tsurime means eyes that look like they're being pulled up by a hook and string or something like that.

Difference between tareme タレ目 and tsurime ツリ目, diagram.

Source: japanesewithanime.com (CC BY-SA 4.0)

Translation

The common term for eyes that have high outer corners in English is "upturned eyes."

A corner of the eye is technically called a "canthus," and a technical phrase for the tareme facial feature is "positive canthal tilt."

Akiyama Mio 秋山澪, example of upturned eyes, tsurime ツリ目.

Anime: K-On!!, Keion!! けいおん！！ (Season 2) (Episode 1)

Round tsurime eyes are also called nekome 猫目, "cat eyes," by the way.

Kurapika クラピカ, example of nekome ネコ目, "cat eyes," eye shape.

Character: Kurapika クラピカ
Anime: Hunter x Hunter (2011) (Episode 40)

Tropes

In anime, characters with tsurime ツリ目 eyes tend to be strong and assertive. They don't hold back at starting fights. They're either serious about something, full of conviction, or are scheming and sadistic. In any case, these are eyes convey hostility.

Jessie, also known as Musashi ムサシ, example of upturned eyes, tsurime ツリ目.

Character: Jessie, Musashi ムサシ
Anime: Pokémon, ポケットモンスター (Episode 8)

The tsurime eyes are also considered to be cooler and more mature-looking. Cooler in the Terminator 2 kind of cooler.

Kohaku コハク, example of upturned eyes, tsurime ツリ目.

Character: Kohaku コハク
Anime: Dr. Stone, ドクターストーン (Episode 7)

otoko-masari
男勝り
Topping men. Winning against men. Refers to female characters that could probably beat male characters in a fight, who're usually deemed unfeminine because of that.
- masaru
  勝る
  To outrival. To win against. To top. To be better than.

Matoi Ryuuko 纏流子, example of upturned eyes, tsurime ツリ目.

Character: Matoi Ryuuko 纏流子
Anime: Kill la Kill, キルラキル (Episode 1)

As one would expect, not all tsurime characters have these traits, but characters that have these traits usually also have tsurime eyes.

Furthermore, characters that have tareme eyes have the opposing type of personality: they're more docile, avoid confrontation, frail rather than strong, and cute rather than cool.

Siblings

A sub-trope is that two siblings, sometimes twins, often sisters, have opposing eye shapes, because they also have opposing personalities, and the eye shapes often reflect those personalities.

Hiiragi Kagami 柊かがみ, and Hiiragi Tsukasa 柊つかさ, example of fraternal twins one with tsurime ツリ目, the other with tareme タレ目.

Left: Hiiragi Kagami 柊かがみ (older fraternal twin)
Right: Hiiragi Tsukasa 柊つかさ (younger twin)
Anime: Lucky☆Star, らき☆すた (Episode 3)

Characters are often designed to fit a dozen of tropes along the plot.

Consequently, the younger sister ends up being the frail, cute one, that gets involved with bad influences, like the main character, while the older sister ends up being the strong, protective one, that tries to keep.her younger sister away from the main character. Or something like that.

Fujibayashi Kyou 藤林杏, and Fujibayashi Ryou 藤林椋, example of sisters one with tsurime ツリ目, the other with tareme タレ目.

Left: Fujibayashi Kyou 藤林杏 (older sister)
Right: Fujibayashi Ryou 藤林椋 (younger sister)
Anime: CLANNAD (Episode 6)

Araragi Tsukihi 阿良々木月火, and Araragi Karen 阿良々木火憐, example of sisters one having tareme タレ目 and the other tsurime ツリ目.

Left: Araragi Tsukihi 阿良々木月火 (younger sister)
Right: Araragi Karen 阿良々木火憐 (older sister)
Anime: Nisemonogatari 偽物語 (Episode 1)

Edward Elric エドワード・エルリック, and Alphonse Elric アルフォンス・エルリック, example of brothers one having tsuri-me ツリ目, and the other tare-me タレ目.

Shorter: Edward Elric エドワード・エルリック (older brother)
Taller: Alphonse Elric アルフォンス・エルリック (younger brother)
Anime: Fullmetal Alchemist: Brotherhood, Hagane no Renkinjutsushi 鋼の錬金術師 (Episode 12)

Narutaki Fuuka 鳴滝風香, Narutaki Fumika 鳴滝史伽, example of sisters on with tsurime ツリ目, the other with tareme タレ目.

Left: Narutaki Fuuka 鳴滝風香 (older twin sister)
Right: Narutaki Fumika 鳴滝史伽 (younger sister)
Anime: Mahou Sensei Negima! 魔法先生ネギま！ (Episode 9)

Ginrou 銀狼, and Kinrou 金狼, example of siblings one with tareme タレ目, the other with tsurime ツリ目.

Left: Ginrou 銀狼 (younger brother)
Right: Kinrou 金狼 (older brother)
Anime: Dr. Stone, ドクターストーン (Episode 7)

Again, it's not like the trope always happens. There are cases where the older sibling has tareme eyes instead.

Sakuranomiya Maika 桜ノ宮苺香, Sakuranomiya Aika 桜ノ宮愛香, and Sakuranomiya Kouichi 桜ノ宮香一, example of siblings with tsurime ツリ目, tareme ツリ目.

Left: Sakuranomiya Maika 桜ノ宮苺香 (younger sister)
Middle: Sakuranomiya Aika 桜ノ宮愛香 (older sister)
Right: Sakuranomiya Kouichi 桜ノ宮香一 (older brother)
Anime: Blend S, ブレンド・S (Episode 9)