This is the 452nd most frequent Czech word.
všem
"Všem" means "to everyone" or "to all" in English.
In this sentence, 'všem' means 'to all' and is used as a dative plural case of 'všichni', meaning 'all'.
Všem lidem na světě přeji mír.
I wish peace to all people in the world.
Here, 'všem' signifies 'to all' and is again in the dative plural case, used to indicate the indirect recipients of the action.
Rozdala dětem všem dárky.
She distributed gifts to all the children.
In this sentence, 'všem' is a part of the phrase 'po všem', where it implies 'after everything'; here, 'všem' is in the locative singular form.