A repeal is the removal or reversal of a law. There are two basic types of repeal. A repeal with re-enactment (or replacement) of the repealed law, or a repeal without replacement.  The move to rescind, repeal, or annul is used in parliamentary procedure to cancel or countermand an action or order previously adopted by the assembly. Removal of secondary legislation is normally referred to as revocation rather than repeal in the United Kingdom and Ireland. Under the common law of England and Wales, the effect of repealing a statute was "to obliterate it completely from the records of Parliament as though it had never been passed." This, however, is now subject to savings provisions within the Interpretation Act 1978.

Partial or full repeals

A partial repeal occurs when a specified part or provision of a previous act is repealed but other provisions remain in force. For example, the Acts of Union 1800, providing for the union between the formerly separate kingdoms of Great Britain and Ireland as the United Kingdom, was partially repealed in 1922. This was when (as a consequence of the 1921 Anglo-Irish Treaty), twenty-six of the thirty-two counties of Ireland were constituted as the Irish Free State, and ceased to be part of the United Kingdom.

A full repeal occurs where the entire Act in question is repealed.

Repeal with or without re-enactment

A typical situation where an Act is repealed and re-enacted is where the law in the area is being updated but the law being repealed needs to be replaced with one suitable for the modern era.  Re-enactment can be with or without amendment. However, repeal and re-enactment without amendment normally occurs only in the context of a Consolidation Bill (a bill to consolidate the law in a particular area).

For example the repeal of the Poor Laws in England in 1948 reflected their replacement by modern social welfare legislation.

A repeal without replacement is generally done when a law is no longer effective, or it is shown that a law is having far more negative consequences than were originally envisioned. Many repeals without replacement are the result of significant changes in society.  Major examples include:
the old Jim Crow laws or blue laws in the US
The Corn Laws in England, repealed in 1846 after a passionate campaign.
Repeal of Prohibition in the United States. Enacted by the Eighteenth Amendment to the United States Constitution, it proved to be so ineffective that it had to be repealed by the Twenty-first Amendment. This is the only constitutional amendment to be repealed in the U.S.
The massive Statute Law Revision Act 2007 in the Republic of Ireland, through which 3,225 Acts were repealed, dating back over eight centuries to 1171 and the earliest laws enacted by England when it began its invasion of Ireland. The statutes repealed include a number of Acts of significant historical interest, including an Act of 1542 providing that the Kings of England shall be Kings of Ireland. This Act is the largest single repealing statute in the history of Ireland.
Don't ask, don't tell was a policy of the US military signed into law by president Bill Clinton in 1993. Service members could not be asked their sexual orientation. They were also not allowed to discuss the subject among themselves. Congress passed a law in 2010 to repeal the policy.

References 

Law
Legal terms