The Three-Fifths Compromise was a compromise reached between the Southern and Northers states during the Philadelphia Convention of 1787. The Three-Fifths Compromise is named such because it entailed that three-fifths of the enumerated slave population would be counted for representation regarding both the distribution of taxes and and approportionment of the members of the House of Representatives.
The Compromise was controversial because those who opposed slavery wished to count only the free inhabitants of each state while those who supported slavery wanted to count the slaves towards their numbers--however, since slaves couldn't vote, the slaveholders would have the benefit of increased representation in the House and the Electoral College. The final compromise of counting the slaves as only three-fifths of their actual numbers reduced the power of the slave states relative to the original southern proposals (counting half the slaves towards their population and later counting three-fourths of the slaves) but increased it over the northern position.
The Compromise had a major effect on pre-Civil War political affairs due to the disproportionate representation of the slave states relative to voters. For example, southerners dominated the Presidency, the Speakership of the House, and the Supreme Court in the period prior to the Civil War.
As is common knowledge, the Compromise was rendered moot following the Civil War and the abolition of slavery by the Thirteenth Amendment.