Why are antibiotics prescribed for rosacea? is it a bacterial infection?

No: The antibiotics decrease bacteria which be a factor but are used more as antiinflammator drugs to decrease inflammation. The drugs decrease activity of white blood cells which are overactive in rosacea.

Can be: Although rosacea is not an infection per se, one of the complications of having it is a form of acne. That form of acne usually responds well to metronidazole. This won't cure rosacea, but it can help decrease the inflammation and superficial skin infections. I don't like oral antibiotics for rosacea and try to limit their use to topical products.