"Cache" can refer to one of many different types of caches that Kodi uses, and most are not directly related to each other.
Unlike other pages on the wiki that describe a specific feature or how to get something done, this page is dedicated to helping dispel some of the myths and mystery around the different types of caches that Kodi uses.
1 Video cache and the source of most "out of cache" messages
The video cache is the most common cache that people talk about when it comes to Kodi. The video cache works by saving a few seconds of video before it is needed, so that if there are small slowdowns or bumps in loading the video, it will not constantly pause while waiting to get enough data to resume playing back. The video cache is normally stored in RAM and erased on the fly, as needed. It requires no user intervention to "empty" this cache.
A warning about the cache filling up does not actually mean that more cache space is needed or that the existing cache needs to be emptied. The warning box is not currently well worded and has lead to a lot of confusion with users. What it means is that the video is loading too slowly for the cache to smooth out all of the bumps, and that the bumps will keep happening due to that low video speed.
Kodi only uses a tiny amount of RAM for the video cache, about 60 MB. This is because Kodi is not currently coded to see if the hardware you are using has more or less RAM, so to be safe only a small amount is assumed to be available. Users are able to increase this amount, and modify how "quickly" it fills up, by following the guide at HOW-TO:Modify the video cache. However, changes to these settings are only helpful for a few situations, such as a network that fluctuates in speed, occasional wifi interference, or a connection that is borderline too slow for video to playback.