Alternative spelling for the more conventional 'Mexico'. In many Central American countries, especially Mexico itself, Mexico and Mejico are interchangeable and are even used in official government business.
The miscable-ness of the two words is because, in most Central American Spanish dialects, the letter 'x' is pronounced (and even sometimes used as) as the Spanish 'j'. In Spanish 'Mexico' and 'Mejico' are pronounced with a softened "Y"-sound as "Me-HI-ko", versus the North American English "Meks-ee-ko".
This style is also seen is other words that contain X's, such as 'Texas' spelled as 'Tejas'.