Shining Eyes

In manga and anime, when a character's eyes shine light—as in: they glow—turning into four-pointed sparkles, it's typically because they've set their eyes on something, like a predator ready to pounce the prey, or because they've just seen or heard something that piqued their interest extremely.

It's usually accompanied by a grin. In some cases, it's just an exaggerated way to draw sparkling eyes.

Left: Shidare Hotaru 枝垂ほたる
Right: Shikada Kokonotsu 鹿田ココノツ
Anime: Dagashikashi だがしかし (Episode 1)

Sound Effect

Sometimes when eyes start glowing there's a sound effect played:

kyuupin
キュピーン
*emitting light* (mimetic word.)

In a phrase it would be used like this:

me ga kyupiin to hikaru
目がキュピーンと光る
The eyes emit light with a kyupiin.
The eyes do a kyupiin as they emit light.

Examples

For reference, some examples:

Left: Shidare Hotaru 枝垂ほたる
Right: Shikada Kokonotsu 鹿田ココノツ
Anime: Dagashikashi だがしかし (Episode 1)

Context: Hotaru, the heir of a snack company, who is fanatical for snacks, introduces herself to Kokonotsu, who says to have heard her family name, Shidare, somewhere.
Hearing that, Hotaru's eyes shine and she starts talking about her family's company's history.

Shibata Genzou 柴田源蔵, example of sparkling eyes.

Left: Shigure シグレ
Right: Shibata Genzou 柴田源蔵
Anime: Hataage! Kemono Michi 旗揚!！けものみち (Episode 8)

Context: Genzou is a wrestler, and a furry, who has been summoned into another world where human-like creatures covered in fur, i.e. "beastmen," juujin 獣人, exist.
They're organizing a fighting tournament among humans, and the idea comes up of inviting beastmen to fight, too.
Hearing that, Genzou's eyes shine as he starts his plans of using wrestling matches as an opportunity to touch the beastmen's fur.

Maria マリア, Ayasaki Hayate 綾崎ハヤテ, example of eyes shining.

Left: Maria マリア
Right: Ayasaki Hayate 綾崎ハヤテ
Anime: Hayate no Gotoku! ハヤテのごとく！ (Episode 21)

Context: Hayate, who is a butler, has been forced to crossdress previously, an event which Maria enjoyed very much and probably awakened something in her.
Now, Hayate has been told that his butler clothes are too formal and he has to wear something else for the day. Hayate interjects asking if he's going to have to crossdress again..
Hearing that, Maria's eyes shine as she imagines Hayate crossdressing. Moments later, Maria thinks to herself "what am I thinking?" and her eyes stop glowing.