Moses saw a new thing - a bush that burned but was not burned up - so he went to investigate. Before coming too close, God told Moses to remove his sandals because he was on holy ground. Then God told him Who He was and what He wanted Moses to do. Moses asked what he should tell the Israelites if they asked him what His name is, so God said “I AM WHO I AM. Tell them I AM sent you.”
After some convincing, Moses went to Egypt and God worked through him to free the Hebrews from being slaves in Egypt.
This name shows me that God is eternal. He just IS. He always has been, and always will be. At any time in or out of history, God is. Not He was or will be, but He always IS.
Read the story of Moses and the burning bush in Exodus 3:1-15.