"Meek" means "humble" or "submissive." Perhaps one might think that the way to get a lot is to be assertive, pushy, and demand a lot. "The meek shall inherit the earth" means that in the end, the earth will belong to people who have been humble, submissive, and undemanding.
It is part of a famous speech by Jesus in the sacred Christian book, the Bible. It's often called "The Sermon on the Mount." It's in the book of Matthew, chapters 5-7. You can find (a choice of!) Chinese translations at biblegateway.com.
It is from a part of the speech called "The Beatitudes" (the blessings): "Blessed are the meek: for they shall inherit the earth.... Blessed are the merciful: for they shall obtain mercy.... Blessed are the peacemakers: for they shall be called the children of God."
Another famous part--I'll quote a modern translation:
'You know that you have been taught, “An eye for an eye and a tooth for a tooth.” But I tell you not to try to get even with a person who has done something to you. When someone slaps your right cheek, turn and let that person slap your other cheek. If someone sues you for your shirt, give up your coat as well. If a soldier forces you to carry his pack one mile, carry it two miles. When people ask you for something, give it to them."
It is part of the culture of the English-speaking world and phrases from it have become part of the language. People will say "Blessed are the peacemakers," or "...to turn the other cheek," or "...to go the extra mile" and won't even necessarily be thinking about the Bible.