The question 'What is Paganism?' is, despite its simplicity, a really good one. I'd have to honestly say that the answers are too many and too varied to satisfy the question. I can only give you my point-of-view.
In my understanding, paganism is both a return to old religions and the development of a new blanket religion. Pagans worship the deities of ancient pantheons from many cultures although the Greek seems the most popular. By choosing particular patron deities, many pagans seek to pursue or associate with more subtle attributes.
On the other hand, paganism is a new, blanket religion. Many pagans strip the ancient religions back to two basic deities, the Lord and Lady. Even those who worship ancient patrons understand the place of these two in the grand scheme of Paganism.
The Lord is known by many names; He is the Hunter, the Green Man and the Lord of Animals. He is the lover-child of the Goddess and He represents death and the sacrifice all beings make. This sacrifice includes the deer dying to feed and clothe the people and the sacrifice of the warrior who gives his life to protect his family. The Lord teaches us to honour the sacrifice of death and to accept that we may be called upon to make that sacrifice ourselves. He is typically represented by the Sun who grows weak in the Winter but returns strong in the Summer.
The Lady is eternal; She is sometimes called the Triple Goddess who has the forms of the Maiden, the Mother and the Crone. She is also represented by the Moon, the body which follows the three stages of Waxing, Full and Waning and has power over the waters of the world. Unlike the Lord, the Goddess is eternal and cannot die. As the Goddess, She gives birth to the God and teaches us about the cycles of life, particularly the responsibilities we face at each stage of life.
Becoming a pagan is really a question of looking within yourself and asking how you feel about the world, the universe and yourself. In truth, some pagans have found the religion by running away from Christianity, however, many more feel the spiritual void of the modern world and seek a reconnection with Nature.
Pagans, in general, feel that the Natural world is sacred and not to be abused or corrupted. Indeed, the God is the Lord of the Wild and many pagans equate the Goddess with Mother Nature; to disrespect the world is to offend the gods. The holidays of paganism are aligned with the equinoxes and solstices of the year. Many pagans like to build a personal altar adorned with natural and sentimental items such as conch shells, antlers, feathers, etc., while others prefer to worship under the night sky.
There are a few myths running about involving paganism. There are also broken stitches in the grand blanket. Personally, I like to laugh at them. However, since some people don't know that much about paganism and can't yet see them, let me spell them out for you.
All-in-all, paganism is a good religion. It is growing stronger by the year and threatens to take its place in Western society. It promises freedom where Christianity promises only guilt. If you think you can handle the responsibility that freedom demands, paganism might be worth a look.