Sometimes you indeed get a crash in MacOSX and the crash reporter tool will show up. There’s an option to send a bug report to Apple and please do that, it creates statistical information good to know about. Anyway, in this dialog you also have the option to look at what caused the crash.
Even if you are no computer geek, with some logic you could isolate what’s happening. For example, try to find the so called stack trace that crashed, that one is indicated in the dump. Then look at the output, this shows what was calling what. In most cases there’s symbolic information in this stack trace. For example, I do think that a majority of crashes inside Logic and Live are related to a faulty plugin. If you see that a certain plug-in is involved, disable it (either using Logic’s AU panel) or then just remove it from the plug-in directory (if not sure, use Spotlight to find the instance). If things work fine, then file a support request to that specific plug-ins manufacturer asking what’s going on. Most likely they know the problem; if not they are happy to know what is not working.
You could also read this somewhat technical Tech Note that talks more about crash reporter tool output.