Laissez-faire is a French term that translates to "let do" and is used when referring to government involvement in affrairs. Consequently, a laissez-faire style of anything means that the government is uninvolved in whatever system is being referred to as laissez-faire.
For instance, in a secular state religion is treated as laissez-faire by the government. People are free to believe and practice as they wish without intereference from the government.
Therefore, in a laissez-faire economy economic transactions in the private sector are unregulated by the government. The government's only involvement is with protecting property rights.
Laissez-Faire was the policy that the only role for the government was to help business when it asked to. This is believed by President Coolidge as well as by many Amercians, that government should be involved as little as possible in the day to day running of the economy, If business men were left alone to make their own decisions, higher profits, more jobs and good wages was the result.
In the 1920s, under Coolidge Laissez-faire contributed to the prosperity of the USA. Low taxes and few regulation = chase profit without the fear of interference