There are multiple origins and meanings for the name:
1. Slavic name (Russian Галина) from ancient Greek (Γᾰλήνη) [Galini] - "serenity, peacefulness, calm, calmness, tranquility, clarity", the female equivalent of the male name Galen
2. Latin, Spanish and Italian name (Gallina) meaning - "hen, chicken, fowl"
3. Derived from the name Helen - "bright"
4. Old English "Gaul"