Brief Summary
The Set-Up
This German Foreign Minister dude named Arthur Zimmermann (we call him Art) sends a message to his German ambassador buddy in Mexico about a new strategy for winning World War I. His note gets intercepted, and nations on at least three continents are not at all pleased with its subject matter.
The Text
Zimmermann suggests that Mexico attack the U.S. as a distraction from all the nasty stuff Germany was planning to do in the Atlantic. As a bonus, maybe they'd get Texas, Arizona, and California. He also implies that Japan could attack the U.S., too, and that Germany would pay for it.
TL;DR
Yo, Mexico, wanna fight the U.S.? xoxo Germany.