Shivering Sea said:

When you buy an embryo, you buy the whole thing, it's buying an unborn foal after all. If you go to the store you can already see how embryos are.

Now, what people offer on the forums is the possibility to create an embryo with the stud of your choice. You provide the straw to the owner of the mare, they will create the embryo and sell it to you.

There are certain limitations to this process that are written on the game guide ;) also, the vet's office also provides some info in the embryo section.