Bihar  is among India's poorest states. It lies on the Gangetic plain, with Uttar Pradesh to its west, West Bengal arching to its south and east, while Nepal is to its north. Jharkhand, the mineral-rich tribal belt, used to be part of the state, but in 2001, it was split to form its own state.
Ancient Bihar was the birthplace of the Maurya Empire, the largest ever to rule the Indian subcontinent, and the site of the Buddha's enlightenment. Unfortunately the Maurya Empire collapsed in 185 BCE, and it's been downhill ever since.
Today Bihar lags behind the other Indian states in human and economic development terms, and is one of the poorest Indian states. Bihar has an urban population of just 15% and the society is mainly agrarian. Northern Bihar is prone to perennial flooding. The state has seen mass migration out of the state in last few decades. Bihar saw the Naxal insurgence in last few decades, especially in Southern Bihar, but the situation has calmed down in recent years. The state has earned a very bad image outside Bihar due to caste based politics and the poor law and order situation.
Bihar is connected by train to all major cities of India. Some good trains to reach the capital Patna are:
Bihar has a terrible reputation for crime and banditry (or dacoity, to use the Indian word), with armed bandits recently taking to hijacking moving trains and nearly 5000 kidnappings recorded in 2007. While reality may not be quite as grim as the horror stories you'll hear from non-Biharis, it's still advisable to keep a low profile and to avoid overnight travel on the roads. A low-level Naxalite insurgency continues to bubble in the southern parts of the state, but the tourist is unlikely to venture into the affected regions.
Public transportation systems, like trains and buses, are generally over crowded. Trains in India are generally prone to theft, so it's wise to lock your luggage to the seat in the carriage and keep more aware than usual.
If you are a foreigner or don't know the local languages do get a local guide. Even otherwise a local guide would make things very easy and convenient for you.