Why is a literacy rate important to a country?

Because diplomats want other diplomats to believe that their country will be a good one in the future.

Literacy of a country's people allows them participate fully in the government (if the government allow it), commerce, and life of the country. It also allows people to better themselves through education and experience. They can see possibilities beyond just what they see around them when they can read. Reading is a base that everything else can build on.