Why does Clary give Lina a bean seed?

In The City of Ember, Clary Laine is an old friend of Lina Mayfleet's father. They worked together in the greenhouses and Clary continued to be a part of Lina's life long after her parents passed away. Lina visited Clary throughout her childhood both for Clary's company and so that she could feel close to her father.
When she is older, Lina visits Clary and asks her if Ember is the only source of light in the world. They have a philosophical conversation about the origin of life, and from her pocket, Clary produces a bean seed. She explains to Lina that the bean seed knows deep inside itself how to create a plant. In comparing the seed to a lamp, Clary explains:

A bean seed isn't connected to anything. Neither are people. We don't have plugs and wires that connect us to generators. What makes living things go is inside them somehow.

Clary gives Lina the seed and a pot and encourages her to plant the seed in some soil, water it every day, and wait to see it grow. While Clary is trying to impart wisdom to Lina, there is more significant symbolism at work. In watching the seed grow, Lina's mind continues to consider the possibilities of the world, and it's through that concentration that she begins to discover the secrets of the city. As the seed finally begins to sprout, Lina starts to put together the pieces of the directions to escape Ember. The sprouting seed represents the sprouting idea and Lina's discovery that the world is larger than she could have ever imagined.