This certificate means that your wife can sponsor you (in Japan even your brother in law, or father in law can sponsor you), and that the Japanese immigration allows you to get a get a spouse visa. To get this spouse visa you have to take the certificate to your Japanese embassy, they will put a put a nice paper in your passport and that is your spouse visa.
With this you can enter the country, but within 90days you have to get your gaijincard... please don't make the same mistakes as I did, show your visa at the airport (I showed my passport and this guys didn't checked my visa so he gave me a 90 days instead of 1 year, and when I applied for a Gaijincard they couldn't give me a proper one, because of the immigration mistake... I needed to send my passport to immigration because of this, bla bla).
I know that some people get a 3 year visa the first time, some only a 1 year visa, so I am not sure about this.
My wife did it in March, and they say it will maximum take 3 months, some will get it within a week, some in 2 months, some in 2.5 month. I think it more depends on how busy the immigration office is.
Let your wife call the immigration office to ask what she has to bring, and you should call to your nearby embassy for official information.