What was the zimmerman note and how did it affect the u. s. decision to enter the war?

The Zimmerman telegram was a note sent by Germany's foreign minister to the ambassador of Mexico, seeking alliance with Mexico against the United States if the US entered the war.  Learning of the telegram increased concerns by the US about Germany's intentions, and led to declaration of war.

Further detail:

The US declaration of war to enter World War I was passed by Congress  on April 6, 1917.

The reasons that led to declaring war:

In January, 1917, Germany had resumed its policy of unrestricted submarine warfare.  Germany had halted its attacks on non-military vessels (which it suspected of carrying military supplies) after the furor over the sinking of the Lusitania in 1915.  But now Germany was resuming attacks by its U-boats.In February, 1917, the "Zimmerman Telegram" was intercepted by British intelligence and shared with the US.  Germany's foreign minister, Arthur Zimmerman, had telegraphed an offer to Mexico's ambassador seeking Mexico's support in war vs. the United States in exchange for getting land back from the US.On April 2, 1917, President Woodrow Wilson made a powerful speech to Congress in which he argued that the nation needed to enter the war "to make the world safe for democracy."  Wilson's speech was powerfully convincing, and four days later, Congress declared war.