I have a small cavity/ hole on pits and fissure of molars that is brown. dentist didn't filled it and said it isn't expanding does this means it is arrested cavity and won't expand? dentist told to brush that certain area properly?

If your dentist examined the lesion and said it did not require attention now, have them keep an eye on it at your semiannual examinations. It may not need to be restored now, but there is no guarantee for future need.

If your Dentist has determined 1) the dental infectio9n is non remission, not invading, 2) you have an effective oral hygiene program, and 3) you see your Dentist at least twice a year to have the area evaluated, by all means follow his/her recommendation.