Mailmen are allowed to walk through your yard when delivering mail to your house.
If you get your mail delivered to your door or at a mailbox slot or mailbox mounted to your house then the mailman or letter carrier can walk through your yard or up to your door to deliver the mail.
Mailmen and letter carries can also walk up to your house to deliver packages if they have them.
Mailmen and letter carries can also walk through your yard to go to the next house, although if there's a sidewalk then the mailman or letter carrier will often go down the sidewalk instead.
But to deliver mail and when they need to walk across or through your yard to perform their duties of delivering mail then they are allowed to legally walk through your yard.