It gave the South greater representation in the House of Representatives.
During that humid Philadelphia summer, when the delegates to the Constitutional Convention were creating a new form of government, there were many disagreements to be settled before they could consider their task complete. One of the more important ones was representation in the lower house of Congress, or the House of Representatives.
Representation in the House was (and is) based on the population of a state. Even though most northern states allowed slavery at that time, they did not want to count the slaves as part of the population when determining a state’s representation in the House. The North believed that since slaves were not citizens and could not vote or own property, they should not be counted.
The South argued and even threatened to walk out of the convention if their slaves were not counted. (This foreshadowed events in the 19th Century, when the South would threaten disunion when they didn’t get their way.)
A compromise was reached. They South could count each slave as three-fifth’s of a person when counting population. Every five slaves would equal three people.
Lest you think this is a trivial thing, Thomas Jefferson won the election of 1800 over John Adams, but if there was no three-fifths compromise, Adams would have won the election. This is because a state gets the same number of electoral votes as it does representatives in the House.