The Wikipedia article on font hinting summarizes it very well:
Font hinting (also known as instructing) is the use of mathematical instructions to adjust the display of an outline font so that it lines up with a rasterized grid. At low screen resolutions, hinting is critical for producing clear, legible text.
A picture is worth a thousand words. The image below shows the same text/font rendered with full hinting (top) and no hinting (bottom).
Simply put, font hinting makes fonts look crisp and thin, and whether this is good or bad is highly subjective. It seems that the vast majority of people simply go with whatever their OS default is and do not care or just cannot tell the difference. Many others dislike font hinting, while others feel that font hinting is the only way to make text easily readable and reduce eye strain. This wiki is dedicated to enabling and supporting font full hinting in Linux.
In Linux, it used to be easy to either enable or disable font hinting, and this worked pretty well out of the box around 2012. However, as the various libraries that deal with font rendering have evolved and diverged, it is now very difficult to consistently enable (or disable) font hinting across the entire desktop.