A patch is a change that is done to a game to change/add/remove content. Patches are done on a very regular basis to many popular online games. Players from LoL are especially used to these as they have been happening since the beginning of League. Over 10 years of patches have led to such changes that early League of Legends is no longer even recognizable as the same game.
When a video game like LoL is around for this many years you can assume that every time a champion is added, a map is changed, anything is updated something can go wrong. Bug fixes are used to fix issues, lag, non functional features, and to improve the overall performance and experience players feel. All bug fixes are generally permanent and help to make the game more solid overall.
Improving the Whole Experience
Patches, bug fixes, adjustments, all of these exist to improve the players experience in the game. Whether you look at the massive map changes in season 4, pushing the game to more modern standards or the complete reworks of champions such as Nunu, Ryze, or Kayle. All of these changes lead to a game that can be consistently modern all while retaining the same player base that has been devoted to the game for years. These reasons all add up to why gamers as a whole should welcome these changes and advocate for changes they think should happen.