This surah takes its title from verse 15, which states: "The only people who truly believe in Our messages are those who, when they are reminded of them, bow down in worship, celebrate their Lord's praises, and do not think themselves above this." Prostration means bowing down completely to the ground (face down) in prayer.
Prayer is one of the "Five Pillars of Islam" and it is called salat. Muslims are supposed to pray five times a day in a very ritualistic manner that involves full prostration and specific prayers. How different this is from modern Christian ideas of prayer, which are more casual. Never in my life have I prayed in "full prostration" mode. It seems really intense, but also potentially really meaningful.
The most intense example of religious prostration I've heard of involves certain Buddhist monks who make a pilgrimage to the Bodhi tree in India where the Buddha was enlightened. These monks travel thousands of miles, over the Himilayan mountains, prostrating themselves all the way. They will take one step, lay face down, get up, take another step, and so on. For literally thousands of miles. Now that is some serious prostration.
