If I'm underweight should I *try* to gain weight?

I'm 13 and I have a BMI of 13.6, which a site I saw said was below the 5th percentile (it didn't say which percentile I was, just that it was below 5). I don't feel unhealthy or weak or anything, but my parents said I should eat more. I already eat until I'm satiated, but should I keep eating after that to gain more weight? Should I eat foods with more calories?