1. The Console is the storage area for the "reports" or logs that are regularly created by the UNIX system processes, as well as enabling you to read the various log files right there in the Console itself.
2. If you click the Logs icon in the toolbar you will find many many logs and other sorts of reports, from the results of tasks formerly known as cron jobs all the way to the kernel panic.log (if you've ever had the misfortune to have one of these). The default log that is displayed when you open Console is the console.log, which is a running account of things the system or a program or process thinks is worth reporting as it happens.
3. UNIX systems are very chatty and fond of telling you not only things that are useful, but also tell you far more than any normal human being would ever want to know about things that make no difference whatsoever to you or your computer. So if everything is working just fine and you launch Console and see half a dozen lines that make no sense, don't worry about it. Here's a sample of what's in my Console window right now:
Mac OS X Version 10.4.8 (Build 8L127)
2007-01-26 21:01:44 -0800
Jan 26 21:01:47 NoobiX ntpdate[129]: getnetnum: "time.apple.com" invalid host number, line ignored
Jan 26 21:01:47 NoobiX ntpdate[129]: no servers can be used, exiting
2007-01-26 21:01:55.321 SecurityFixer[222] No insecure startup items found!
2007-01-26 21:22:50.791 Metadata Examiner[235] Could not connect the action showPrefsWindow: to target of class MDAppController
2007-01-26 21:22:50.791 Metadata Examiner[235] Could not connect the action changeMyFont: to target of class MDAppController
2007-01-26 21:39:52.111 VitaminSEE[248] Closing document!
2007-01-26 21:39:52.114 VitaminSEE[248] Destroyed!
2007-01-26 21:39:52.114 VitaminSEE[248] Deallocating window!
The first line tells me something I already know, ditto for the second line. The next two, about ntpdate, apparently refer to the automatic network time that I have set being unable to do something or other. Since my clock is working fine there's no reason for me to care. I guess I'm glad to know that "No insecure startup items found!"--though I'm not as joyous as SecurityFixer is (an exclamation mark? why?) since I haven't added any startup items in forever. Evidently something is wrong with the Metadata program I use, but since it works fine I really don't care. And why the VitaminSEE program got so excited when I closed its window and quit it I don't know, nor care. However, if you open Console and see hundreds of lines being generated every few seconds you've got a problem--not only is something not working right, but it is creating a huge log file. I've heard of runaway log files actually filling a hard drive so that there is no more room for anything else. One of the most notorious was/is the Canon scanner button manager error: Looking for devices matching vendor ID=1193 and product ID=8718, which repeats endlessly.
4. So if you see repeating messages you'll need to do two things: first, run the UNIX maintenance scripts to compress your log files, and then try to find out what is sending the messages and why, and what you need to do to make it stop.
5. The next item in the Logs list is the system.log, which is a report of what your computer is doing as it starts up, with major errors appended to it as you do things on your computer. This can also have both useful information and alarming items that mean nothing at all. If you are having a problem you might be able to find out why, and if you see some messages repeating over and over you'll need to compress your logs to recover hard drive space and then figure out what is causing the problem and fix it.
6. Potentially the most useful are the things in the CrashReporter folder: hit the disclosure triangle for ~/Library/Logs, and then the CrashReporter folder. Click on a crash.log to view it. I can sometimes spot something odd in a crash report, but your best bet is to send the whole report, from the Date/Time of the crash all the way down through the binary images, to someone very expert or post it in Apple Discussions as a question.
7. If you take a look in /var/log you can find out just what it is those UNIX maintenance jobs actually do: their reports appear in daily.out, weekly.out and monthly.out, and you will also see when they have been run. For most of you the most important aspect is compressing logs, removing old logs and deleting other junk. For me, I appreciate having the locate database updated (it is one of the weekly jobs), since I do sometimes use the locate command in Terminal. And you can run these yourself in Terminal whenever you want.