The Senate has the following "executive powers"
1) Ability to impeach a government official.
2) Ability to investigate wrongdoings of a government official (like the President).
In the impeachment process, the House of Representatives is the group of people who can officially charge a person with a crime. The Senate, on the other hand, conducts the actual impeachment trials. The Senate acts like the judge and jury does in a normal court case. In this scenario, the House of Representatives would be the prosecuting lawyer.