When you run LaTeX it gives you lots of information about what it is doing. You can usually ignore this, which is just as well given how quickly it flies across the bottom panel, but sometimes LaTeX will give a warning or an error that you should probably read. A warning is something that LaTeX doesn't like, or isn't sure about; an error is something that stops LaTeX from producing a file.
Severe errors (for example, if LaTeX can't find the file you've asked it to use) will stop LaTeX immediately. Any other warnings or errors will be summarised at the end of the LaTeX output.
When you build your LaTeX file it produces the PDF file you want - however it may also produce several other files, depending on what you've told LaTeX to do. It will always produce a log file, and an auxiliary aux file.
The log file contains all the information that flew past the screen when you built the file. It is very useful when you're trying to find LaTeX warnings or errors.
The aux file contains lots of information on your document that other programs can use. It won't mean much to you, but is very useful so don't just delete it!
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