Dressing "conservatively" means that you wear clothes that:
have an older, more formal style (like a suit and tie for men)
don't display parts of your body like your chest, legs, stomach, or butt
You can also dress "formally", but that's different. People only dress formally on special occasions like ceremonies. A formal dress for a woman is long and expensive. A man who's dressed formally might be wearing a tuxedo.
On the other hand, some people dress "conservatively" every day.