The introduction of a strict code of laws to govern the populace and its interaction with the central power puts an end to many abuses of power and translates immediately into a more stable society. The people express their gratitude by undertaking great works of culture in the empire's main cities - thus the first four of these receive a free cultural building.
Legalism is a great Policy for early development. Your first four cities will get a free Monument (or an Amphitheater, if you constructed a Monument already), and start expanding borders immediately! Not only that, but you will be able to build other buildings and/or units, instead of losing time to build Monuments. So, rush the Policy (by opening the tree, then adopting Oligarchy), unless you intend to build one of the early Wonders.
Legalism does not apply retroactively, and constructs the first building in the culture chain that hasn't yet been constructed in each city (the Monument, Amphitheater, Opera House, Museum, and Broadcast Tower, in that order). If you haven't researched the technology necessary to unlock the building, it will appear once the research is finished.
Buildings received from Legalism do not cost maintenance, but if a city already has the relevant culture building when the policy is enacted, the cost still applies. Because of this, it may be advisable to hold off on building culture buildings in your first few cities. This will save you a substantial amount of gold in the long run.
Legalism is a policy in which the relationship between the ruler and his or her subjects is laid out in a series of laws, which both sides must adhere to strictly. If the law is fair and is properly enforced, the people will be content and the ruler's position will be secure. While this may seem to cover most governments that follow the rule of law, legalism almost achieved the status of a state religion in China during the Warring State Period.