The main logging infrastructure on android — LogCat — is essentially a circular buffer (of limited size) stored in /dev/log/main. Debugging tools can sip into it. In order to keep a longer sequence of entries it needs to be connected to adb or a similar system. Apps like alogcat can display the log without having some other computer tethered.
Details are available on this blog.
Aslak Johansen's Weblog 