The Japan Government advise that:
"A Certificate of Eligibility is issued before a visa application by a regional immigration authority under the jurisdiction of the Ministry of Justice (listed in Appendix 2) as evidence that the applicant fulfills various conditions of the Immigration Control Act, including those certifying that the activity in which the foreigner wishes to engage in Japan is valid and comes under a status of residence (excluding Temporary Visitor Status).
The Certificate of Eligibility has the advantage of reducing the time required to obtain a visa and complete immigration procedures, since a foreigner in possession of such a certificate can probably acquire a visa at an embassy or consulate without any inquiries being made to the Ministry of Foreign Affairs and, by showing the certificate to the immigration officer, obtain landing permission more easily."
Any more questions about the Japan certificate of eligibity, please post your question here.

FYI: My Certificate of Eligibility took almost 2 months to process. >_<

really?

Canada takes about 3-4 weeks, it depends where you live I think because they have to investigate you. Toronto Canada did mine really fast, at least for the time it took....although I hate waiting.