One of the historical events that Martin Luther King Jr. discusses in his speech is the signing of the Declaration of Independence. He argues that, when this was signed, a whole range of rights and duties fell upon every American citizen. He argues that, for African Americans, this was equivalent to a check that could not be cashed due to "insufficient funds."
The reference allows us to place the civil rights movement within this historical context. King argues that, even though equality and the pursuit of happiness are promised in the document, Black Americans do not have access to it. It helps the reader better understand the grievances that African Americans complain about.