CrazyHarry's summary of SCD is pretty good, but not quite correct about the cheese issue.
Actually, there's quite a long list of cheeses that you can eat as much as you want of even on SCD - they are in the back of the last edition of the book, "Breaking the Vicious Cycle." There's also a list of cheeses you can eat, but only in moderation. And then there are the forbidden cheeses, like mozarella. If you are thinking of going on the SCD diet, read the book, first. To make sure you fully understand it.
The following web site also tells you which cheeses are OK for SCD on the legal/illegal list:
Elaine, the author of "Breaking the Vicious Cycle," passed away before she was able to resolve the question of how long cheese needed to be aged in order to get rid of lactose.
Lactose is not allowed on the SCD diet. This is partly why yogurt is aged 24 hours - to get rid of the lactose (the good bacteria eat it). So what we do is buy cheese aged 6 months or longer, like Manchego.