I'm assuming you mean the Levellers of the English Civil War.

The term Leveller is somewhat misleading in that it refers to a broad panoply of radicals, public intellectuals, religious groups, and reformers. The term itself was somewhat pejorative, used by political opponents to castigate the movement (one Leveller leader, John Lilburne, preferred to use "Agitator"). They were a minority within the growing political sphere, but a very vocal one. It's hard to nail down their exact doctrines given their heterogeneous nature; some Levellers believed in property rights as a basis for citizenship, others went further and argued that all English males had a right to citizenship. An even smaller minority wished to extend political and legal equality to both women and children.

The height of the Leveller movement was in the spring of 1647 when it managed to gain significant inroads within the New Model Army's ranks and officers. The army was unpaid, facing an imminent disbandment, and marched upon London after news of Lilburne's arrest for his radical activities. Cromwell tried to defuse this tense situation by listening to the demands of the New Model Army. This resulted in an highly spirited debate within the army in which it articulated its desire for an equal suffrage, parliamentary reorganization, and a recognition of the inalienable rights of all Englishmen. These demands, known as the Putney Debates, drew largely from the ideas of the Levellers' pamphlet An Agreement of the People.

Cromwell took these demands and opted to kill them by committee. Under a Parliamentary commission, it took some of the demands to heart such as a limitation on the powers of parliament to impress civilians or act contrary to law. However, Cromwell's agents within the committee drew a line against certain Leveller tenets such as the expansion of toleration to Catholics.

By the time the committee gave its recommendation later that year, the Levellers' power had dissipated. A series of non-political mutinies gave Cromwell the pretext to reassert greater political control over the army and cashier Leveller officers. Additionally, the threat of the Levellers allowed for Cromwell to unite the more moderate and conservative factions behind him. The Levellers found themselves increasingly marginalized under the Protectorate.

Part of the appeal of the Levellers is that they offered a political program that was not taken. Since they were such a diverse political lot, they provided an ideological parentage for many radicals and political agitators of the coming century.

Sources

Davis, J. C. Oliver Cromwell. London: Arnold, 2001.

Purkiss, Diane. The English Civil War: Papists, Gentlewomen, Soldiers, and Witchfinders in the Birth of Modern Britain. New York: Basic Books, 2006.

Woolrych, Austin. Britain in Revolution, 1625-1660. Oxford: Oxford University Press, 2002.