Dichoso translates to "blessed" or "fortunate." It's a beautiful and somewhat less common word than simply saying "happy" (feliz).
In the song, Juan Luis Guerra sings, "me siento dichoso contigo, de tantos ser yo el elegido" (I feel blessed with you, out of so many to be the chosen one). This word perfectly captures the profound sense of gratitude and joy he feels for his love, elevating the emotion beyond simple happiness.
Juan Luis Guerra's "Muchachita Linda" is such a sweet song, all about being completely smitten! He's dancing bachata with his "muchachita buena" [good girl] and it's clear she's everything to him. He says she's "vida para mi" [life for me] and the "flor que sueño en mi jardín mujer" [flower I dream of in my garden, woman].
He feels so lucky, like out of everyone, he was chosen "para recibir la promesa de tu amor" [to receive the promise of your love]. Her laughter "corona la ilusión" [crowns the illusion] and even dictates his heartbeat! He repeats her name over and over, calling it "la mas fiel respuesta de mi fe" [the most faithful answer to my faith]. The bachata itself becomes a metaphor for her love, wrapping him "en la piel de una nube con manto de estrellas" [in the skin of a cloud with a mantle of stars]. It's a beautiful, heartfelt declaration of love, where his world literally revolves around her – he even says "la tierra gira cuando me hablas tu" [the earth spins when you speak to me].