The LaTeX system has 3 levels of messages and TeX itself has another 2.
- LaTeX Error ... stops the processing because something is seriously broken. Sometimes it is possible to continue but in most cases it is best to correct the error directly and reprocess the document
- LaTeX Warning ... is only displayed on the terminal and in the transcript file and processing continues. Something is wrong with the document and it needs some level of attention. The issue may be temporary, the best example is "Rerun to get cross-references right" or it may be something that you decide to ignore because it visually doesn't matter (e.g., "Float too large by 3pt"), but it should preferably be a conscious decision. A few of the LaTeX warnings are related to obsolete syntax. In all cases (in theory at least) the warnings are things that you can and should ignore until you are nearly finished with document writing. Otherwise you may end up fixing things that go away by themselves due to rewriting your text.
- LaTeX Info ... this is an informational message (sometimes helpful in debugging) that is only written to the transcript file. Those you can normally ignore.
Instead of "LaTeX Error/Warning/Info" it may say "Package..." or "Class..." if the message is generated out of a package or class file.
As LaTeX is a system with a huge amount of packages built by different developers the above classification may not always be 100% obeyed, as different people may have different opinions on what is a warning (that can wait for resolving) and what is an error that needs immediate attention, but on the whole (and for the kernel and core packages) this classification is valid.
In addition TeX also generates error and warning messages with more or less the same ideas as above. The main difference is that the format of the error/warning messages are slightly different, i.e., no prefix like "LaTeX Warning:". It is a bit unfortunate that the TeX program has no method to trap these and present them as "LaTeX..." but most of them are generated when you have no control over the processing, so that's why both flavors exist.
So in summary:
- address errors immediately
- resolve warnings only when you are really finished writing your document, and then make a conscious decision if you will ignore the warning (such as "Overfull hbox 0.3pt" or fix it, because you will feel offended by the typographical glitch even if it is small). Several if not most of the warnings you better fix at this point, because they effectively mean there is still something typographically or semantically wrong with your document.
For the LaTeX Companion, 2nd ed I wrote an appendix that explains all Error and Warning messages of the LaTeX kernel and its major packages. I ended up with about 60 pages explaining what the likely causes are and how to fix them. For those who can read French there is an
online version of this appendix in French available.