How do I determine what is locking up my machine?
That message means that there is a kernel panic. This may happen if you connect new hardware to your computer. For possible reasons/fixes, see this article from the Apple website. Here is a section from the "Troubleshooting" section...


Was the computer starting up, shutting down, or performing a
particular task when the recurring kernel panic happened?
Is the kernel panic intermittent, or does it happen every time you do
a certain thing?
Does it occur only when a certain external device is connected, or
a device is connected to a certain port?


Reading through that article should give you a general idea what is happening and possible ways to fix it.