Hi, Eugene! "You have my word" is an idiomatic expression. It shows a promise or a vow, so essentially it means "I promise that I will do a particular thing." It's actually stronger than "I promise" because, historically, a person took an oath of honor when they said this. Nowadays, we don't use this phrase in a typical conversation. You can find it in books and films set in old or medieval times. I hope this helps, and please feel free to ask me more questions. Best Regards, Teacher Ariana www.italki.com/englishwithariana

Also, this question should be: "What does it mean?" or "What does 'You have my word' mean?"