My brother has infection around eye. Is that something important?

Yes. If it's not getting better on it's own or worsening. Our immune system can take care of some infections. Other fast progressing or non healing infections are more serious and need to be diagnosed correctly after evaluation.
Always. Infection in any part of the body is important. It must be recognized, evaluated and the proper treatment administered. Fortunately we have an arsenal of effective anti-infective agents for most of these and results are usually good. Eye infection is important as it usually is obvious, mostly uncomfortable and can be visually threatening. Hopefully your brother is on treatment.