Slavery was prominent in the South. Southern states wanted to count enslaved African Americans as part of their populations. This would give these states more votes in the House of Representatives. At the time, there were more than 550,000 enslaved African Americans. Counting them would add many representatives. The North, however, had fewer representatives. The enslaved people couldn't vote or participate in government. The North didn't want them to be counted.
The 3/5 compromise meant that every five enslaved persons would equal three free persons. This was effective because the North and South had equally gained what they had wanted- enslaved persons to be counted or not to be counted. (This rule was applied for assessing taxes on the states as well)
Hope this helped :)