Fangirl energy, is the energy that girls who obsess over certain boys or TV or movie characters get when they are obsessing over them, or when an episode with the character they obsess with is on.
Example 1:

Grace: "Oh my gah dude Lloyd Garmadon looks even more Squeekawaii now that he's older!"
Cealia: "Dude, calm down. You're building up too much Fangirl energy, you might explode.
Example 2:

Grace: *SQUEAL!* "Yes! That episode of Fairly Odd Parents, 'Country Clubbed' is on! REMY BUXAPLENTY IS SO FRICKIN CUTE I WILL NAO EXPLODE WITH FANGIRL ENERGY!"
by Kawaiikitsune August 22, 2014
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