Why does legislative branch of the government represent the people most directly?

It legislates, wich means it passes laws.
When the U.S. Constitution was written, the House of Representatives was designed to represent the people, with the seats divided up in proportion to each state and their population. House members are voted into office by the people in their districts and are naturally closer to the people who elected them. The framers wanted the Senate to be a check on the common folk in the House, so the Senate was comprised of elite, educated men who were chosen by the state legislatures. Nowadays, the Senate is also voted in by the people, albeit a more homogenous group since the voter pool is comprised of the entire state and not just a single district, like the House.