As an au pair, you'll be living with a family and mainly working with and looking after the family's children. You may also be expected to do a certain amount of housework and take on some of the responsibility for the children's education, whether you simply help them with homework or actually give lessons of your own. In this sense, the job borders on that of a governess. The fact that you live with the family helps offset the fairly low pay you might expect, as you won't have to worry about rent, food or bills (so it's worth it just for the stress relief).
Traditionally, an au pair is someone from a foreign country, so you should check up on visas and working rights in the country you intend to visit. Some countries in fact have visas specifically for aux pairs (this is the correct plural of 'au pair', which is nice to know), whereas others require simply a general, temporary working visa or even no visa at all. Whatever the situation, you'll definitely need to find out about it first, to avoid any trouble later on.
Obviously the main responsibility of an au pair is to look after children. For this reason, you must enjoy working with children, otherwise being an au pair really isn't the job you! Any job working with children requires someone with a calm and patient manner and demeanour. You may also have to do some housework (like doing the children's laundry) and other household tasks. Bear in mind also that, as an 'extra parent' of sorts you may have to work long and unusual hours.