Referenda are an electoral device in America that allow voters to veto a bill passed by a local/state legislature. Like initiatives and recall elections, referendas are seen as an extension of democracy. In Britain, local councils etc., once voted in, can pass bills with little external input or hindrance from those who elected them in to power (especially if such bills are unpopular).
In theory, referendums in America allow just such an input into local affairs after elections and make local politicians more accountable to those they represent. However, referendums cannot be used for what are deemed emergency and financial bills.
The process of a referendum is relatively straight forward.
Any legislation passed at a state/local level comes into being usually 90 days after it has been passed.
During this 90-day period, a bill may be suspended if someone who objects to it, gets the required number of names on a petition. The suspended bill is then voted on by those registered to vote and if the majority vote against the bill, it is killed off.
A constitutional referendum is specific to proposed changes in a state's constitution.
An advisory (or optional) referendum is where a legislative body might volunteer proposed legislation to those in their electoral area to vote on i.e. a legislature will pass a bill (delayed for 90 days) and then asked those in the electoral district to vote on it. In this way they get popular support for legislation due to be enforced in a locality or state.