The verb moteru モテる means "to be popular [with girls or guys]." Someone who's moteru-ing in anime is someone surrounded by wannabe girlfriends/boyfriends. that receives a dozen of love letters a day, and that most likely is either a bishounen 美少年 or a bishoujo 美少女.
(do not mistake moteru モテる with ninki 人気 that's used for things that are "popular", like popular mangas, animes, and games)
Just in case you have some doubt of what it means to motenai, in the anime Watashi ga Motenai no wa Dou Kangaetemo Omaera ga Warui! 私がモテないのはどう考えてもお前らが悪い! a.k.a. WataMote ワタモテ, a.k.a. "No Matter How I Look at It, It’s You Guys' Fault I’m Not Popular," the character Kuroki Tomoko 黒木智子 does not moteru, that is, she motenai, she's not popular.
Not everyone wants to be moteru, but those who do "want to be moteru" motetai モテたい. That is, a way to say "I want to be popular with girls (or boys)" in Japanese is just the word motetai. The -tai is a conjugation form that means "I want to [verb]"
That said, just because you motetai doesn't mean you will moteru..
(motenee モテねー is another way to say motenai)
Lastly, if you've ever had the