What is the meaning of the lotus?

The lotus flower sits atop the water but is not moistened by it. It gets its water from roots embedded below the water.

The analogy implies we can be in this world yet free of worldly desires.

The already submitted answers explain the symbolism of the lotus very well. I'd like to add some important references to the lotus in Buddhism.

I'd often seen the lotus used in Mahayana Buddhist art such as this painting of Amitabha:

The Lotus Sutra is an important Mahayana sutra studied by numerous schools.

Om mani padme hum is a well known mantra which is translated various ways but a well known translation is "Praise to the Jewel in the Lotus."

The lotus holds an important place in Pure Land Buddhism as seen in this excerpt from the translator's introduction to The Three Pure Land Sutras:

The Buddha told Ānanda to worship Amitāyus. At once Amitāyus manifested himself with a majestic appearance and his light shone everywhere, so that Ānanda and all the others in the assembly clearly saw the Pure Land. They witnessed two types of birth: 1) that of those born from within the lotus flowers, and 2) that of those remaining in the lotus buds. Those aspirants who have accepted the Buddha’s wisdom with pure faith are to be born by instantaneous transformation and fully enjoy the highest bliss, but those with doubts must remain in the lotus buds for five hundred years (section 43).

But I wondered about the importance of the lotus in my own tradition of Theravada and whether there were references to the lotus in the Pali Canon. Here's what I found:

From AN 4.36

"Just like a red, blue, or white lotus — born in the water, grown in the water, rising up above the water — stands unsmeared by the water, in the same way I — born in the world, grown in the world, having overcome the world — live unsmeared by the world. Remember me, brahman, as 'awakened.'

"The fermentations by which I would go to a deva-state, or become a gandhabba in the sky, or go to a yakkha-state & human-state: Those have been destroyed by me, ruined, their stems removed. Like a blue lotus, rising up, unsmeared by water, unsmeared am I by the world, and so, brahman, I'm awake."

From Samyutta Nikaya 22:94:

"Just as a water-lily or a blue lotus or a white lotus, born in water, growing in water, having arisen above the water stands unwetted by the water, similarly, bhikkhus, the Tathaagata, brought up in the world and conquering the world,[64] lives unsullied by the world."[65]

This poem by the Elder Udayin from the Theragatha

As the flower of a lotus,

Arisen in water, blossoms,

Pure-scented and pleasing the mind,

Yet is not drenched by the water,

In the same way, born in the world,

The Buddha abides in the world;

And like the lotus by water,

He does not get drenched by the world.

The translator's note from the above poem states:

Awakening (represented by the lotus blossom) is something that happens again and again in all different places and times, and is not limited to a single occurrence of it among the Sakya's of ancient India.

The various Buddhist traditions don't agree on everything. But the usage of the beautiful lotus flower as a symbol for enlightenment cuts across traditions.

Well there are more than one meaning to the lotus image. It is a multi-layered symbol.

http://buddhists.org/buddhist-symbols/the-meaning-of-the-lotus-flower-in-buddhism/ the meaning of the muddy waters, physicality being the ground out of which the nirvana experience grows.

The lotus flower represents one symbol of fortune in Buddhism. It grows in muddy water, and it is this environment that gives forth the flower’s first and most literal meaning: rising and blooming above the murk to achieve enlightenment.

and the second meaning refers to how the pure flower is when its roots are in the mud and the earth

The second meaning, which is related to the first is purification. It resembles the purifying of the spirit which is born into murkiness.

Rather than faithfulness to a doctrine, what it implies is faith in the process so that at all points of development from a shoot out of the mud, to blooming, it is the process of awakening. The third meaning refers to faithfulness. Those who are working to rise above the muddy waters will need to be faithful followers [of the process] (note added by soulsings)

Each color implies a different quality of the buddha mind.

The color bears importance in the meaning of the lotus flower in Buddhism. A white lotus flower refers to purity of the mind and the spirit. If a lotus flower is red, it refers to compassion and love. The blue lotus flower refers to the common sense; it uses wisdom and logic to create enlightenment. The pink lotus flower represents the history of Buddha and the historical legends of the Buddha. A purple lotus flower speaks of spirituality and mysticism. Finally, the gold lotus flower represents all achievement of all enlightenment, especially in the Buddha. and regarding colors also see http://www.buddhanet.net/e-learning/history/b_lotus.htm

and the symbolism of the stages of growth.

The stage of growth the lotus flower is in represents a different stage of enlightenment. A closed lotus flower represents the time before a Buddhist follower found Buddha or enlightenment. A lotus flower fully bloomed and open represents full enlightenment and self-awareness.

Rising out of the mud of materiality into the emotions (represented by the water) the path of awakening eventually leads to the opening of the lotus flower before the sun of compassion and wisdom.