Presumir means "to boast" or "to show off." While it can sometimes have a negative connotation, in this song, it's used in a very sweet and endearing way.
Lenin Ramírez sings, "Y presumir que por ti soy un loco enamorado" (And to boast that because of you, I am a crazy in love man). Here, he's expressing a desire to proudly declare his intense love, not in an arrogant way, but as a joyful declaration of his feelings. It's a unique and charming use of the word.
Have you ever been so head-over-heels for someone that you just want to shout it from the rooftops? That's exactly the feeling Lenin Ramírez gives us in "Quédate"! This song is a sweet, direct confession of love, where he's practically bursting with excitement. He tells his love, "Como puedo explicarte mi niña / Que me siento enamorado" [How can I explain to you, my girl / That I feel in love], making it clear his feelings are overwhelming.
He's totally charmed by everything about her, from her "locuras, tus manías de esa linda sonrisita" [craziness, your quirks, that pretty little smile] that brightens his days. He wants to share his whole life with her, whispering sweet nothings, stealing a thousand kisses, and showing her how amazing it is to be in love. He even wants to brag that he's "un loco enamorado" [a crazy in love man] because of her. It's a really heartfelt and adorable plea for her to stay and be his forever!