As the name states, giving a loved one this flower means “forget me not.” Often gifted between lovers when they would be separated for a length of time, but also used as a token of affection between friends.
From Floriography: An Illustrated Guide to the Victorian Language of Flowers:
“The forget-me-not’s name and meaning originate with a German folktale about a young couple in love. While walking along a river, the bride-to-be stops to admire a cluster of beautiful blue flowers. Her lover attempts to pick the flowers for her, but he falls into the swiftly flowing river. He throws the flowers to her as the river carries him away, calling out to her ‘forget me not!’”