This word comes from barba (beard) + the suffix -ita. In Spanish, this suffix is a "diminutive," which can mean something is small, but it's often used to show affection or cuteness.
In the song, Shakira sings "Me gusta esa barbita" ("I like that little beard"), pointing out a small, specific detail that she finds charming about the person she's falling for. It's a perfect example of how a simple word can be filled with affection and personality.