Our bicameral legislature is the result of the 1787 Great Compromise (Connecticut Compromise).
During the constitutional convention, large and small states worried about proportional representation. Large populous states like Virginia and New York favored a single House of Representatives, where legislative representation would reflect states' overall Population. Small states like Connecticut and Rhode Island favored a senate where each state had a fixed number of representatives so that smaller states would have equal footing as large states. Small states opposed a single house of representatives and large states opposed a single senate, so a compromise to institute both legislative bodies was reached.
Our legislature is also split up to divide legislative responsibilities. The House was envisioned as a space for non-elites who would represent their state, while the Senate would consist of educated elites who would decide matters brought up in the House and settle matters related to foreign policy and war. The House could also be seen as a check on elite power in the senate, as it has the power to levy taxes and spend federal money. (the power of purse).