Essentially, modern neo-druidry is an earth-centred spiritual practice, usually (though not always) with a Celtic theme. There are lots of differences between the practices and beliefs of individual druids, but harmony with the natural world, ecology, respect for one's ancestors and the spirits of the land are common themes. Modern druids are also associated with poetry, music and storytelling, natural magic and seasonal rites.
Modern druidry is a continuation from a Victorian romantic imagining of what ancient druidry was and what ancient druids did. We know really very little about ancient druids, and what we do know was recorded by Greek and Roman historians who weren't privy to druidic teachings. There's nothing definite in the way of archaeological evidence for their practices or beliefs.
However, drawing from the Greek and Roman writings, historians think that the druids were some kind of priestly class for the ancient Celts, especially in Wales where there was a bardic college apparently located on Anglesey before it was destroyed in the 1st century AD. Julius Caesar wrote that the druids were concerned with priestly duties, the observation of the stars, natural history and that they were lore-keepers for their people. They were more or less wiped out as a religious cultus by the 2nd century while under Roman rule.
The 18th century saw a revival in the interest of pre-Christian Britain as a response to industrialisation, and writers began to imagine what druids must have believed and practiced. This is where modern neo-druidry draws most of its information from and where druid orders like OBOD sprang out of.
For more information take a look at;
The Path of Druidry, by Penny Billington
Blood and Mistletoe, by Ronald Hutton
Natural Druidry, by Kristoffer Hughes
The Book of Druidry, by Ross Nichols