Which branch can confirm appointments?
The Legislative Branch confirms appointments by the President. In particular, the Senate has the power to consents or confirm appointments.
The Senate has the power to confirm presidential appointments to the Supreme Court. This is an example of what principle of US government?
Checks and balances. The Executive branch has power over (checks the power of) the Judiciary branch by way of choosing who to appoint. The Legislative branch has power over (keeps in check) the Judiciary branch by way of choosing whether to confirm the appointments. The Legislative Branch also has power over (keeps in check) the Executive branch because the appointments to the Supreme Court require their approval.
In order to ensure that only qualified people are appointed to federal positions, it is important that a president not have unlimited power to make various appointments. The right of the Senate to confirm presidential appointments is one of the most important ways that the legislative branch can have a check on the executive branch so that the executive branch does not become too powerful in relation to the legislative and judicial branches of government.