Yes, he is running for re-election.
2012 only
Since U.S. presidents can not serve more than two terms, when Barack Obama's second term ends, he will no longer be able to run for president. In November 2016, there will be an election, and a new president will be chosen.
He ran from the state of Illinois. He had been a U.S. senator from that state before running for president.
Barack Obama became president in 2008. He then ran for re-election and won a second term in 2012. When his term ends, he will not be able to run for a third time, because presidents are only allowed to serve two terms.
Yes, she did in 2008, losing the primary to Barack Obama, and again in 2016, losing the general election to Donald Trump.
He has to run first.
The reason Barack Obama became so famous was because of the fact that he was African American. He was a very competent candidate for presidency as it was, but the fact that an African American was able to successfully run an election process actually boosted his popularity.
Barack Obama has never been a cabinet secretary. He ran for Illinois state senate in 1996, and served three terms. He then became a U.S. Senator, and in 2008, he was elected president.
Hillary Clinton ran for the Democratic position in the 2008 Presidential election but lost to Barack Obama. She is rumored to run again in 2016.
The United States is a democracy. This means candidates run for election (some countries say they "stand" for election) and then, the citizens vote. In 2008, Barack Obama was elected president when he received more votes than his challenger, John McCain.
Actually, Barack Obama first ran for the state senate in his home-state of Illinois. It was 1996 and he was a lawyer and a law professor at that time, but he had a history of working with the poor; and according to his writings, he has said he decided he could make more of a difference if he were in politics. He ran a good campaign and was elected to the Illinois State Senate. In 2000, he did try to run for US Representative, but he lost-- it was the only election he ever lost. He was elected to three terms in the state senate, and he then ran for the US Senate (and won) in 2004.