Yarhamuk Allah يرحمك الله means May Allah have Mercy on you, Yarham is from Raham (mercy).
When someone sneezes they should says "Alhamdulilah""Al Hamdulilah" and when you witness this should you say "Yarhamuk Allah".
Abu Huraira reported Allah's Messenger (ﷺ) as saying:
Six are the rights of a Muslim over another Muslim. It was said to him: Allah's Messenger, what are these? Thereupon he said: When you meet him, offer him greetings;when he invites you to a feast accept it. when he seeks your council give him, and when he sneezes and says:" All praise is due to Allah," you say Yarhamuk Allah (may Allah show mercy to you) ; and when he fails ill visit him; and when he dies follow his bier.