Some other things to consider about that reference:
1) It represents an example of "jingoism" - where extreme patriotism or nationalism is used to motivate a population towards a foreign policy goal, usually war. "Remember the Lusitania" and "Remember Pearl Harbor" are other examples. (see link below)
2) At the time and for a long time after the Spanish were blamed for sinking the ship. This was in no small part to the yellow journalism of William Randolph Hearst, newspaper magnate, who famously said: "You give me the pictures, and I'll give you a war". (Also linked)
3) Recent historical and forensic research has led to the conclusion that the Maine sank when a coal fire ignited the gunpowder in her magazine, thus having nothing to do with the Spanish. See the Random House article for more informaiton on this.
The USS Maine was a battleship sent to Havana, Cuba to protect American people and property from harm during a rebellion against Spanish rule in 1898.
While in Havana harbor, the Maine blew up. At the time, it was believed that Spanish saboteurs had blown the ship up and illustrations were printed in American newspapers detailing how the alleged sabotage had happened.
Americans were outraged by this apparent Spanish atrocity and the incident led directly to the US declaration of war against Spain (Spanish-American War). The slogan "Remember the Maine" was used to whip up fervor for the war by reminding Americans of the need for revenge.
It is to stir up feelings and sentiments of the American public to support the war effort against the Spanish.