The word on the street was that Nixon was too publicly corrupt, and Eisenhower was going to have to drop him as a running mate (historians believe Eisenhower was set to do it). Nixon gave this speech, telling the American people to contact Eisenhower with their opinion, thus effectively removing from the presidential candidate the option to drop him by implying it was up to the American people.

From Wikipedia:

Nixon, having been accused of accepting $18,000 (which equates to approximately $140,000 in 2007 dollars) in illegal campaign contributions, gave a live address to the nation in which he revealed the results of an independent audit that was conducted on his finances, exonerating him of any malfeasance. The money, he asserted, did not go to him for personal use, nor did it count as income, but rather as reimbursement for expenses. He followed with a complete financial history of his personal assets, finances, and debts, including his mortgages, life insurance, and loans, all of which had the effect of painting him as living a rather austere lifestyle. He denied that his wife Pat had a mink coat, instead she wore a "respectable Republican cloth coat."

The one contribution he admitted receiving was from a Texas traveling salesman named Lou Carrol who gave his family an American Cocker Spaniel, which his daughter named "Checkers." [2] Nixon admitted that this gift could be made into an issue by some, but maintained that he didn't care, stating "the kids, like all kids, love the dog and I just want to say this right now, that regardless of what they say about it, we're gonna keep it." Later, when asked about Nixon's performance, some Dwight Eisenhower campaign insiders joked, "We're keeping the dog." (Mentioning the dog was a subtle way of attacking the Democratic party. During World War II, Republicans charged that FDR had accidentally left his dog Fala behind on the Aleutian Islands while on tour there, and had sent a United States Navy destroyer to retrieve him at an exorbitant cost.)[3]

Nixon then challenged Democratic Presidential candidate Adlai Stevenson to give a similar public account of his finances, and attacked alleged corruption in the Truman administration. Furthermore he accused Truman's foreign policy of being a failure that led to the Korean War. He ended with an appeal to the public to wire and write to the Republican National Committee to give their advice on whether he should remain the Vice-Presidential nominee.

The speech was simulcast on radio and was a resounding success overall. Nixon, whom many expected to be dropped from the ticket, gained widespread sympathy and remained Eisenhower's running mate.