Lyanna Mormont is Jon Snow's daughter. Jon was romantically involved with Maege and as a result, she gave birth to a girl child. She was black haired like her father. Maege didn't want the world to know that the child is of a Snow's. However, due to her love for Jon, she named the child after his mother, Lyanna. Jeor Mormont was aware of all this.
As he hoped that one day Jon would take care of Maege and their child, he entrusted him with their ancestral sword, Longclaw. Unfortunately, Maege died trying to protect Jon's family during the red wedding. It was a deeply emotional moment when Jon and Lyanna met because neither of them knew they were father and daughter.
How did Jeor know about the affair? Pfffft... Bear Island has ravens.
Why doesn't Jon know about this child? Pfffft.... He knows nothing.
How did Maege know about Lyanna Stark? Pfffft... D&D told her.