Logs

What is a Log?

A Log in the context of Minecraft and some programs is a file that is created and written by a program or in this case, Minecraft, and used to store information about what is going on behind-the-scenes. They are extremely helpful for locating errors and other issues.
Minecraft generates three different types of logs, which are detailed below. Some mods may generate their own log files.

Latest Log

The latest.log can be found in the logs directory in your Instance. This log is automatically generated every time you launch the game, and every mod can write to it, including errors.
When you launch the game and the latest log already exists from a previous session, it will be compressed to .gz.

Crash Report

Crash Reports are generated when Minecraft experiences a fatal error. They can be found in the crash-reports directory in your Instance. They are named after the date and time of the crash, making it easy to find the latest crash report.
Crash Reports often contain useful information about what happened and why, but not everything. This is why it's often good practice to provide your latest.log alongside your crash report if you're having a problem.

The crash-reports directory only generates when a crash occurs, so if you cannot find the directory, you did not experience a crash.

Debug Log

The debug.log can be found in the logs directory in your Instance. This log is automatically generated every time you launch the game, and every mod can write to it.
When you launch the game and the debug log already exists from a previous session, it will be compressed to .gz like the Latest log.

This log often contains extra details that don't need to be written to the Latest log. It is very helpful to include this log when reporting an issue with a Mod.

Some Launchers have a toggle to enable / disable this log, such as the CurseForge launcher. If you cannot find this log, check your Launcher settings to see if it is disabled.

What to do with a log?

If you are asked to provide a log, here's what you should do to give whoever helping you an easier time:
Locate your log in your file manager, and drag it into this website: mclo.gs and select Save. When it finishes, copy the link in the address bar and paste it to whoever is helping you. This website formats certain parts of the log for readability, and identifies any errors.
Alternatively you can use a site like pastebin or gist.github, but they will lack the formatting.