I couldn't miss the chance to practice my drawing!
Menu grinding refers to the act of changing set-ups for characters before entering a battle, often a boss battle, or a particular location. This often implicates basic things like restoring HP, but can also extend to switching equipment to suit elements or protect against statuses, changing job classes, or switching abilities. Menu grinding is more necessary if a player has not sufficiently leveled up.
In job system games where characters can switch classes, switching to the White Magic ability to use restorative and curative spells without needing it to take a slot during battles is a common technique players use.
In the Lodestone Cavern of Final Fantasy IV where metallic weapons do not work, and in Ipsen's Castle of Final Fantasy IX where weapons with a lower Attack power are strongest, the player is required to switch their weapons to best make it through the dungeon.
In Final Fantasy VIII, the player may take SeeD quizzes in the menu to increase salary, and spells junctioned may be modified to suit the desired stats.
In Final Fantasy XII, the player has access to the menu during battle, which allows one to change equipment for each individual enemy attack. This can be used to absorb or block all elemental attacks and defend against various status effects without having one single piece of equipment that is effective against all elements or statuses.
In Final Fantasy XIII, player's health is restored after every battle, removing much of the ability to menu grind, but the player is given a chance to tweak their paradigms to suit the upcoming battle situation.