In its modern usage, a "clean sweep" most often means to win everything. The phrase might be used to describe an awards ceremony where one person wins in every category. It is also commonly used to describe political victories, especially one in which a candidate runs in multiple districts or states and wins the majority of the vote in each area.
As a phrase used by sailors, clean sweep means to vanquish an enemy. In the case of such a victory, sailors once hung a broom from the highest point of the vessel to indicate to others that they had been victorious. Also in nautical terms, sailors might describe a clean sweep as an instance in which waves washed onto the deck of the boat, soaking everything left behind and taking with them or moving anything that was not tied down.
Although clean sweep in its modern usage is most often used to refer to a complete victory, it is still sometimes used in the older sense of the original proverb. It can be used to mean a fresh start, in which a person gives up old habits, possessions, or relationships in order to begin anew. The proverb dates to the 19th century, and a phrase even older, general sweep, dates to the 16th century. General sweep had much the same connotation and usage as the proverb and the idiom clean sweep.
The phrase likely developed at the time when brooms were made at home or by a local craftsman. Made of dried grasses or twigs that were lashed together, the making or purchasing of a new broom wouldn't happen often because of the work involved. A broom was used until it was worn out, and when a new broom was made, it would make a clean sweep of dust and dirt that had accumulated once the old broom had become too worn to be effective.
As with many old phrases, clean sweep has found its way into entertainment, art, and even government. The phrase has lent itself to the title of a television show and a Hardy Boys novel. It is also the name of a type of Microsoft computer software.