"Dead Presidents" is slang for money, since that's what appears on most US currency. The term was popularized in a 1995 movie of that name, but has been used by rappers for some time, notably in the 1987 track "Paid In Full."
This samples a Q-Tip remix of "The World Is Yours" by Nas. After this was released, Jay-Z and Nas had one of the longest feuds in rap history. Jay made note of the sample in his song "Takeover" with the lyrics, "I sampled your voice, you was usin' it wrong," and went on to dig Nas for not taking control of his business affairs, as the money Jay paid for the sample went to a publishing company Nas didn't own.
Like many of Jay-Z's songs, this recounts life as a street hustler rising to stardom. While embracing his roots has given him tremendous street cred, Jay recognized that his feud with Nas was getting dangerous, and in 2005, he performed this song with Nas at the "I Declare War" concert to formally ended the feud.
The beat was sampled from Lonnie Liston Smith's song "A Garden of Peace."
The album version is listed as "Dead Presidents II," and has different lyrics than the single. but different lyrics.
Suggestion credit: Donovan Berry - El Dorado, AR, for above 2