The primary purpose for a bicameral legislature is to dilute the effects of the popular will in decision making for a state or country by creating more hurdles for legislation to clear before becoming law and/or by creating one house of the legislature that does not go through direct election. The British Parliament and the original makeup of the United States Congress both fulfilled this purpose.
The British Parliament features the House of Commons and the House of Lords. While the House of Commons consists of members who are directly elected by the public, the House of Lords consists of hereditary peerages. In the past two centuries, limits have been placed on the House of Lords so that the House of Commons has more power in the creation of laws.
In the original United States Constitution, members of the Senate were to be named by state legislatures, and each state received two. State legislators were elected by residents of each state, but senators were not directly accountable to their voting public for election. When some states left Senate vacancies open for months or years because of infighting and it became clear that many senators were simply there to protect private interests, momentum grew for the 17th Amendment, which changed senatorial election to a direct vote.