First, please note that we can only answer one question at a time on eNotes, so I have picked one of the questions to answer and edited out the rest.
The veto is the power that the president has to reject any bill that Congress passes. In almost all cases, a bill only becomes a law if both houses of Congress pass it and the president signs it. (It is also possible for the president to refuse to sign it but let it become law anyway.) The president has the power to reject any bill, though a two-thirds vote of both houses of Congress can override his (or someday her) veto and pass the bill over the president’s veto.
The implication of the veto is that it makes for a stronger executive by giving the executive a check on the legislature. The Framers of the Constitution were very concerned that one part of the government might get too much power. Therefore, they wanted to create checks and balances so that the various branches could rein each other in. The veto power allows the president to do this. It gives the president a way to stop the Congress from doing something that the president thinks is bad. It also gives him a way to pressure Congress (through threat of veto) to create bills that are acceptable to the president. This gives the president an important check on the legislative function of Congress.