Broad church is a term referring to latitudinarian churches in the Church of England. After the terms high church and low church came to distinguish the tendency toward Anglo-Catholicism, on the one hand, and Puritanism, on the other, those churches tolerant of multiple forms of conformity to ecclesiastical authority came to be referred to as "broad." As the name implies, these churches will mix high and low forms, either eclectically or depending upon priest. The emphasis is on allowing individual parishoner choice.
Nancy Mitford is alleged to have said that the three types of service one finds in the English church are "High and crazy, low and lazy, broad and hazy."
To his astonishment the local Church of Scotland minister who himself is a fine evangelical preacher was unable to give that guarantee as he felt that he would have to invite another C of S minister to preach – even though he knew that this man was not an evangelical.
Sadly the Free Church man felt he had to withdraw because he could not participate in a service where people were being invited to hear the gospel, and yet it could not be guaranteed that the gospel would be preached.
Broad churchmanship (whether it is Calvinistic or not) does not work and will not work because it is not radical enough and because it is an old fashioned answer to an old fashioned problem.
Dr. South says, The High Church are those who think highly of the Church and lowly of themselves; the Low Church, those who think lowly of the Church and highly of themselves (this may be epigrammatic, but the latter half is not true).
BroadChurch are those who think the Church is broad enough for all religious parties, and their own views of religion are chiefly of a moral nature, their doctrinal views being so rounded and elastic that they can come into collision with no one.
It is also called the Roman Catholic Church, to distinguish it from the Anglican Church or Anglican Catholic Church, a branch of the Western Church.