Timed Hits appear in every Mario RPG, but mainly in Super Mario RPG: Legend of the Seven Stars, because there are a lot of them. An example of an attack that needs timing is Super Jump. The weapons can do a big or small amount of damage, depending on if they are timed right, or not.
A "Timed Hit" means that the player must push a specific button (Paper Mario series) or any of the letter buttons (A, Y, Z, X). As mentioned in the above, when a hit is timed right, the spell or weapon does more damage.
There are five types of timed hits in total. 1-Level Hits, 2-Level Hits, 3-Level, Multi-Level Hits and Control Pad Action Hits (Super Mario RPG only).
These are the most common types of Timed Hits. For these to work, the player must push a button only once. The Jump attack in Paper Mario uses this.
These aren't so common. Attacks that use this timing level must be timed two times to work. They're also used for 2-Hit Attacks, which hit an enemy two times, but they require timing for each for increased damage.
These aren't common, too. Attacks that use this timing levels must be timed three times. Time Level 3 is also used for 3-Strike Attacks, in which the attacks are repeated three times, but the player needs to time every single strike.
These types of hits are common. Attacks that use them must be timed four or more times. These are also used when an attack repeats four or more times, but every repeat must be timed. Examples are Super Jump (Super Mario RPG) and Star Rain (Super Mario RPG).
Control Pad Action Hits (Super Mario RPG only)
To time these attacks right, the player is given a heads up at the top of the screen on what to do.
Rotate Control Pad
To get the timing right on this particular type, the player should begin at the Up portion of the D-Pad, then go counterclockwise to each direction.
Hit Y Rapidly
These attacks require pushing the Y button as quickly as possible. Getting the timing is simple. The more the button is pushed, the more damage the move inflicts.
Almost all of Geno's spells use this. Three stars build-up at the bottom of the screen on their own (the player does not determine their appearance as it is automated). Depending on when the player starts holding Y and when they release it, the spell's power is determined. For example, holding Y throughout all three stars causes Geno Beam to do only basic damage with no additional strength. To get the most out of this, the player should release the Y button the instant the third star appears.