Fall damage is one of the basic mechanics of the game where a character sustains damage from falling from too high. The Player only takes damage after falling past a certain threshold, at which point the damage taken is linear with the distance traveled past said threshold (and not related to speed).
Negation
There are two major ways of negating fall damage.
Stopping the Fall
The first and most obvious is to "break" the fall before hitting the ground. The Fall Damage taken is literally calculated by the fall distance (and not speed). Using items such as Cloud in a Bottle, Rocket Boots, Grappling Hook or Ivy Whip will cause the "fall distance" counter to reset upon use, negating the damage.
Preparing the Terrain
An other alternative is to prepare the terrain in such a way as to not take Fall Damage at all: Placing wooden platforms inside shafts guarantee the player cannot not fall more than 25 blocks. Other alternatives include cushioning the ground: Cobwebs or just Water will stop the player's fall, without damage.
Calculations
You will not receive fall damage until you drop beyond 25 blocks (50 feet). At 26 blocks (52 feet) you receive 10 damage with no equipment. Every block above that is an additional 10 damage, or 5 damage every foot. Example: You drop down 50 blocks that is 250 damage.
You can create an equation from this:
(a - 25) * 10 = b
Where:
a = Blocks above ground level (where you land)
b = Fall damage
Again, you have to be ABOVE 25 blocks to receive any fall damage at all.
Also, defense plays a roll in how much damage you take.
Defense's equation is very simple. You take the defense of your armor/accessories and divide it by two then round up (at least in the case of fall damage). Example: You have 19 defense, you'll divide this by two (9.5) and round up (10). So if you fall 50 blocks you'll take 240 damage instead of 250 damage.
This makes the Fall Damage equation:
((a - 25) * 10)) - ceiling(b / 2) = c
Where:
a = Blocks above ground level (where you land)
b = Total Defense
c = Fall damage
ceiling = Round up
Maximum Fall Damage
Maximum Fall Damage
Although there is no maximum cap on fall damage, there is a limit to how big your map is.
On a large world you can take up to 23270 damage if falling from the top of the map to the bottom. This would mean falling down 2352 blocks (after 25 blocks). So from the bottom of the map to the top of the map (that a player can have access to) is 2352 blocks + 25 + 2 (because you land on your feet, you have to account for your body and head too) which makes a large world 2379 blocks in height, or 4758 feet.