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Both "la bailarina" and "el bailarín" are forms of "bailarín", which is often translated as "dancer". Learn more about "bailarín" below.
el bailarín, la bailarina, bailarín()
This means that the noun can be masculine or feminine, depending on the gender of the noun it refers to (e.g., el doctor, la doctora).
1. (profession)
b. ballet dancer (in ballet)
Él tiene un carrera exitosa como bailarín clásico.He has a successful career as a classical ballet dancer.
c. ballerina (feminine, in ballet)
Mi sobrina sueña con ser bailarina y bailar El Lago de los Cisnes.My niece dreams of being a ballerina and dancing in Swan Lake.