Erase Macbook using Find my Iphone

Someone stole my fiancé's MacBook. I went into Find My iPhone and selected the option to erase it but I am curious when the device will actually be erased. Will it erase whenever the thief opens the lid or will the thief have to log into the computer and select a wifi point to log into? The reason I ask is because today it says it was erased, and I really need to know if they were able to login to my computer (yes there was a password on the log in screen).