These are phrases used to at the beginning or end of meals and
mean something like "have a good meal" / "enjoy your meal". There
is no exact English equivalent of this, though some people
say bon appetit, particularly in restaurants.
Many people say grace, a short prayer recited before or after
a meal to invoke a blessing upon the food or to give thanks for it.
(douzo meshiagare) = 'enjoy your meal' - said by the cook/chef いただきます
(itadakimasu) - said before a meal by those eating it ご馳走さまでした
(gochisōsama deshita) - said after a meal by those who have eaten it