Unanimous consent is an agreement by all members present on anything requiring a yes or no decision. If a family all agrees to have pizza for dinner, this can be considered unanimous. If anyone objects to pizza, however, unanimous agreement is not achieved, and the decision may have to come down to either a vote or parental discretion. In Congress, unanimous consent is a way of quickly deciding issues without taking a vote. Issues where unanimous agreement may be readily obtained are noncontroversial ones.
For example, if Congress wishes to table an issue and no one objects, this move can be considered unanimous. Alternately, Congress might decide to have Democrats and Republicans take turns arguing an issue. Though the issue itself may not be agreed on unanimously, the procedure for arguing the issue may be.
At times, all members present in Congress approve bills or confirmation hearings without objection. When most of Congress knows something will be approved with unanimous consent, there's no good reason to take a vote. Generally, a statement first calls for any objections to be raised. If no objections are raised, no vote is needed, so whatever decision needs to be made is adopted unanimously.
Unanimous consent in Congress saves time for the debates and votes needed on issues likely to spark controversy. It helps that a bi-partisan Congress can agree on certain things in order to get on with the real debates.
If any member of Congress objects to an action, it cannot pass unanimously. So, for example, it is unlikely that decisions like confirmations of Supreme Court Justices or amendments to the Constitution will be made without a vote.
In rare situations, as after the 11 September 2001 attack in the US, Congress adopted several measures by unanimous consent because there was a great deal of support for the president and his party. Several months after 9/11, however, party divisions began to reassert themselves, and issues once again became more likely to be voted on.
One further distinction in unanimous consent in Congress needs to be made. It can only refer to the members of Congress who are present. A person who objects to something but who is not there to object essentially has no vote, and is not considered in the decision.