The Zimmerman telegram was a note sent from Germany to Mexico, offering money and weapons to help Mexico gain back control of the American Southwest. Mexico declined the Zimmerman telegram, for a number of reasons. A major reason would be that if Mexico accepted this help, it would mean declaring war on the United States. Previously, Mexico had cooperated with Argentina, Brazil, and Chile to prevent the declaration of war on the United States. Mexico knew that accepting the Zimmerman telegram would cause poor relationships with countries they had just repaired their relationship with.
Mexico also chose not to accept the Zimmerman telegream because the resources the Germans offered would not be enough the regain control of the American Northwest. The United States was the only nearby country where arms were manufactured and Mexico would not be able to purchase arms from them. Germany could also not send weapons because the British were in control of the English seaways and would prevent the weapons from arriving in Mexico. Finally, there was now a sizeable English population living in the American Northwest, which the Mexicans would not be able to control.
To summarize, Mexico declined the Zimmerman telegram because they did not want to create strained relationships with other countries, they did not have access to enough weapons to defeat the Americans, and they would not be able to control the English population currently living in the area.