The Senate is more prestigious and more powerful than the House. While there are hundreds of congresspeople in the House of Representatives, there are only 2 senators for every state. By dint of their being only 100 of them, each one has more power. Each one is accountable to a state rather than a small congressional district.
The Senate must also vote for the country to legally declare war, although that has been made a little blurry in recent times. As someone above stated the three branches of government are to provide a checks and balances for our government.
Certainly the Senate plays an important function within the mechanics of American government, being a body that ratifies a number of different other functions, such as the appointment of federal judges and ambassadors as well as treaties. You might want to think about how it acts as a check or balance of power.
I'll add two more duties exclusive to the Senate. In addition to voting on Supreme Court justices, the Senate must vote to confirm all federal judges and all ambassador appointments made by the President.
Are you asking for more of these? If so, they also have the right to vote on appointments to the President's cabinet and on people appointed to lower courts. Another important responsibility they have is voting on treaties -- a treaty can't go into effect if they reject it.
The US senate acts as a legislative body in conjunction with the House side to enact laws on behalf of the US government. The Senate contains 100 members and serves longer terms than the House of Representatives. The Senate also acts as the advice and consent function for many presidential appointments and conducts activities as prescribed by the US Constitution.