The primary purpose of the 3/5ths Compromise was to solve the "issue" of whether or not slaves would count towards a states population. At the time of this compromise, slaves were still considered property rather than people.
On one hand, you wanted Southerners to count slaves towards the population, as this increase in population would result in an increase in representation in the House of Representatives. Northerners did not want slaves to count for the same reason, as it would give Southern states more political power in passing federal laws.
To make both sides content, the 3/5ths compromise was introduced. This stated that every 5 slaves will count as 3 people towards a states population for the purposes of taxes and determining a states representation in the House.
